Maximality of noncommutative rings over orders
La teoría de órdenes ha sido ampliamente estudiada desde la última parte del siglo XX. En el contexto no conmutativo, la maximalidad de órdenes ha sido revisada para objetos clásicos de tipo polinomial como las extensiones de Ore y las extensiones PBW, entre otras, y más recientemente para anillos d...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/75731 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/75731 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemáticas Order Maximal order Ore extension PBW extension Skew PBW extension Ore-Rees ring Orden Orden maximal Extensión de Ore Extensión PBW Extensión PBW torcida Anillo de Ore-Rees |
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Maximality of noncommutative rings over orders |
| title |
Maximality of noncommutative rings over orders |
| spellingShingle |
Maximality of noncommutative rings over orders Rodríguez Rodríguez, Camilo Andrés Matemáticas Order Maximal order Ore extension PBW extension Skew PBW extension Ore-Rees ring Orden Orden maximal Extensión de Ore Extensión PBW Extensión PBW torcida Anillo de Ore-Rees |
| title_short |
Maximality of noncommutative rings over orders |
| title_full |
Maximality of noncommutative rings over orders |
| title_fullStr |
Maximality of noncommutative rings over orders |
| title_full_unstemmed |
Maximality of noncommutative rings over orders |
| title_sort |
Maximality of noncommutative rings over orders |
| dc.creator.none.fl_str_mv |
Rodríguez Rodríguez, Camilo Andrés |
| author |
Rodríguez Rodríguez, Camilo Andrés |
| author_facet |
Rodríguez Rodríguez, Camilo Andrés |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Reyes Villamil, Milton Armando |
| dc.subject.none.fl_str_mv |
Matemáticas Order Maximal order Ore extension PBW extension Skew PBW extension Ore-Rees ring Orden Orden maximal Extensión de Ore Extensión PBW Extensión PBW torcida Anillo de Ore-Rees |
| topic |
Matemáticas Order Maximal order Ore extension PBW extension Skew PBW extension Ore-Rees ring Orden Orden maximal Extensión de Ore Extensión PBW Extensión PBW torcida Anillo de Ore-Rees |
| description |
La teoría de órdenes ha sido ampliamente estudiada desde la última parte del siglo XX. En el contexto no conmutativo, la maximalidad de órdenes ha sido revisada para objetos clásicos de tipo polinomial como las extensiones de Ore y las extensiones PBW, entre otras, y más recientemente para anillos de Ore-Rees. En este trabajo extendemos algunos resultados encontrados en la literatura a las extensiones PBW torcidas. |
| publishDate |
2019 |
| dc.date.none.fl_str_mv |
2019-07-31 2020-02-25T16:57:26Z 2020-02-25T16:57:26Z |
| dc.type.none.fl_str_mv |
Trabajo de grado - Maestría info:eu-repo/semantics/masterThesis info:eu-repo/semantics/acceptedVersion http://purl.org/coar/resource_type/c_bdcc http://purl.org/coar/version/c_ab4af688f83e57aa Text |
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masterThesis |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/75731 |
| url |
https://repositorio.unal.edu.co/handle/unal/75731 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
[AAMAI11] A. Amir, P. Astuti, I. Muchtadi-Alamsyah, and I. Irawati. On maximal orders and factor rings of Ore extension over a commutative Dedekind domain. Far East J. Math. Sci., 55(1):21–30, 08 2011. 9 [AHK17] A. Alhevaz, E. Hashemi, and K. Khalilnezhad. (Σ,∆)-compatible skew PBW extension ring. Kyungpook Math. J, 57(3):401–417, 2017. 14 [AHK19] A. Alhevaz, E. Hashemi, and K. Khalilnezhad. Extensions of rings over 2-primal rings. Matematiche, LXXIV(I):141–162, 2019. 14 [AL15] J. P. Acosta and O. Lezama. Universal property of skew PBW extensions. Algebra Discrete Math., 20(1):1–12, 2015. 14 [AM03] E. Akalan and H. Marubayashi. Multiplicative ideal theory in noncommutative rings. Mathematical Notes, 74(3):401–410, 2003. 36 [Art15] V. A. Artamonov. Derivations of skew PBW extensions. Commun. Math. Stat., 3(4):449–457, 2015. 14 [BG88] A. Bell and K. Goodearl. Uniform rank over differential operator rings and PoincaréBirkhoff-Witt extensions. Pacific J. Math., 131(1):13–37, 1988. II, 1, 10, 11, 34 [CH80] A. W. Chatters and C. R. Hajarnavis. Rings with chain conditions. Chapman & Hall, 1980. 25 [Cha81] M. Chamarie. Anneaux de Krull noncommutatifs. J. Algebra, 72(1):210–222, 1981. 9, 27, 28 [Coh50] I. S. Cohen. Commutative rings with restricted minimum condition. Duke Math. J., 17(1):27–42, 1950. 26 [ER70] D. Eisenbud and J. C. Robson. Hereditary Noetherian prime rings. J. Algebra, 16:86– 104, 1970. 28, 36 [Faj19] W. Fajardo. A computational Maple library for skew PBW extensions. Fund. Inform., 167(3):159–191, 2019. 15 [GHK19] M. Ghadiri, E. Hashemi, and K. Khalilnezhad. Baer and quasi-Baer properties of skew PBW extensions. J. Algebr. Syst, 7(1):1–24, 2019. 14 [GL11] C. Gallego and O. Lezama. Gröbner bases for ideals of σ-PBW extensions. Comm. Algebra., 39(1):50–75, 2011. II, 14, 15 [GL16] C. Gallego and O. Lezama. d-Hermite rings and skew PBW extensions. São Paulo J. Math. Sci., 10(1):60–72, 2016. 14, 15 [GL17] C. Gallego and O. Lezama. Projective modules and Gröbner bases for skew PBW extensions. Dissertationes Math., 521:1–50, 2017. 15 [HHR19] M. Hamidizadeh, E. Hashemi, and A. Reyes. A classification of ring elements in skew PBW extensions over compatible rings. 2019. Submitted. 14 [HL72] C. R. Hajarnavis and T. Lenagan. Localisation in Asano Orders. J. Algebra, 21:441–449, 1972. 27 [HMU16] M. Helmi, H. Marubayashi, and A. Ueda. Ore-Rees rings which are maximal orders. J. Math. Soc. Japan, 68(1):405–423, 2016. II, III, 12, 13 [JL16] H Jiménez and O. Lezama. Gröbner bases for modules over σ-PBW extensions. Acta Math. Acad. Paedagog. Nyházi. (N.S.), 31(3):39–66, 2016. 15 [JR18] J. Jaramillo and A. Reyes. Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions. Ingeniería y Ciencia, 14(27):29–52, 2018. III, 16 [KMU85] Kazuo Kishimoto, Hidetoshi Marubayashi, and Akira Ueda. An Ore extension over a v-HC order. Math. J. Okayama Univ., 27:107–120, 1985. 23 [Kuz72] J. Kuzmanowich. Localizations of Dedekind prime rings. J. Algebra, 21(3):378–393, 1972. 27 [LAC+13] O. Lezama, J. P. Acosta, C. Chaparro, I. Ojeda, and C. Venegas. Ore and Goldie theorems for skew PBW extensions. Asian-European J. Math., 06(04):1350061, 2013. 24 [LAR15] O. Lezama, J. P. Acosta, and A. Reyes. Prime ideals of skew PBW extensions. Rev. Un. Mat. Argentina, 56(2):39–55, 2015. 14, 15, 22 [Lez16] O. Lezama. Cuadernos de Álgebra, No. 9: Álgebra no conmutativa, volume 123. SAC2, Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, 2016. http://sites.google.com/a/unal.edu.co/sac2. 29, 30, 31, 32, 33, 34, 35 [Lez19] O. Lezama. Computation of point modules of finitely semi-graded rings. Comm. Algebra, 2019. https://doi.org/10.1080/00927872.2019.1666404. 14 [LG19] O. Lezama and J. Gómez. Koszulity and point modules of finitely semi-graded rings and algebras. Symmetry, 11(7):1–22, 2019. 18 [LR11] L Levy and C. Robson. Hereditary Noetherian Prime Rings and Idealizers. American Mathematical Society, 2011. 9 [LR14] O. Lezama and A. Reyes. Some Homological Properties of Skew PBW Extensions. Comm. Algebra, 42(3):1200–1230, 2014. II, 14, 16, 17, 18, 19, 20, 22 [LRS15] O. Lezama, A. Reyes, and H. Suárez. Some relations between N-Koszul, ArtinSchelter Regular and Calabi-Yau algebras with skew PBW extensions. Ciencia en Desarrollo, 6(2):205–213, 2015. 16, 18 [LV17] O. Lezama and H. Venegas. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry. Discuss. Math. Gen. Algebra Appl, 37(1):45–57, 2017. 14 [Mar80] H. Marubayashi. Polynomial rings over Krull orders in simple Artinian rings. Hokkaido Math. J., 9:63–78, 1980. 27 [Mar83] H. Marubayashi. A Krull type generalization of HNP rings with enough invertible ideals. Comm. Algebra, 11(5):469–499, 1983. 25, 27, 28 [Mar84] H. Marubayashi. A skew polynomial ring over a v-HC order with enough v-invertible ideals. Comm. Algebra, 12(13):1567–1593, 1984. 24 [McC74] J. McConnell. Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture. Proc. London Math. Soc., s3-29:453–484, 1974. 10 [Mic69] G. O. Michler. Asano orders. Proc. London Math. Soc., 3:421–423, 1969. 27 [MR01] J. McConnell and J. Robson. Noncommutative Noetherian Rings. American Mathematical Society, 2001. II, 1, 2, 3, 4, 5, 6, 7, 8, 9, 32, 33, 35 [MU17] H. Marubayashi and A. Ueda. Examples of Ore extensions which are maximal orders whose based rings are not maximal orders. J. Algebra, 479:368–379, 2017. II, III, 9, 10 [MYZ98] H. Marubayashi, P. Yang, and Y Zhang. Some examples of PBW extensions which are Krull orders. Math. Japonica, 1998. 36 [MZ96] H. Marubayashi and Y. Zhang. Maximality of PBW extensions of orders. Comm. Algebra, 24(4):1377–1388, 1996. II, III, 10, 11, 21, 22, 23, 24, 25, 26, 28 [NR17] A. Niño and A. Reyes. Some ring theoretical properties of skew Poincaré-BirkhoffWitt extensions. Bol. Mat., 24(2):131–148, 2017. 14, 21 [Ore33] O. Ore. Theory of Non-Commutative Polynomials. Ann. of Math., 34(3):480–508, 1933. II, 8 [Pas87] D. S. Passman. Prime ideals in enveloping rings. Trans. Amer. Math. Soc, 302(2):535– 560, 1987. 11, 17 [Rey13] A. Reyes. Ring and Module Theoretical Properties of skew PBW extensions. PhD thesis, Universidad Nacional de Colombia, Bogotá., 2013. II, 16, 18 [Rey14] A. Reyes. Uniform dimension over skew PBW extensions. Rev. Col. Mat., 48(1):79–96, 2014. 16, 34 [Rey15] A. Reyes. Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings. Rev. Integr. Temas Mat., 33(2):173–189, 2015. 17, 19 [Rin63] G. S. Rinehart. Differential forms on general commutative algebras. Trans. Amer. Math. Soc., 108(2):195–222, 1963. 10 [RR19] A. Reyes and C. Rodríguez. The McCoy condition on Skew Poincaré-Birkhoff-Witt Extensions. Commun. Math. Stat, 2019. https://doi.org/10.1007/s40304-019-00184-5. 14 [RS16a] A. Reyes and H. Suárez. Armendariz property for skew PBW extensions and their classical ring of quotients. Rev. Integr. Temas Mat, 34(2):147–168, 2016. 21 [RS16b] A. Reyes and H. Suárez. A Note on Zip and reversible skew PBW extensions. Bol. Mat, 23(1):71–79, 2016. 14 [RS16c] A. Reyes and H. Suárez. Some remarks about the cyclic homology of skew PBW extensions. Ciencia en Desarrollo, 7(2):99–107, 2016. 14 [RS17a] A. Reyes and H. Suárez. Bases for quantum algebras and skew Poincaré-BirkhoffWitt extensions. Momento, 54(1):54–75, 2017. III [RS17b] A. Reyes and H. Suárez. Enveloping algebra and skew Calabi-Yau algebras over skew Poincaré-Birkhoff-Witt extensions. Far East J. Math. Sci., 102(2):373–397, 2017. 18, 21 [RS17c] A. Reyes and H. Suárez. PBW bases for some 3-dimensional skew polynomial algebras. Far East J. Math. Sci. (FJMS), 101(6):1207–1228, 2017. III, 18 [RS17d] A. Reyes and H. Suárez. σ-PBW Extensions of Skew Armendariz Rings. Adv. Appl. Clifford Algebr., 27(4):3197–3224, 2017. 21 [RS18a] A. Reyes and H. Suárez. A notion of compatibility for Armendariz and Baer properties over skew PBW extensions. Rev. Un. Mat. Argentina, 59(1):157–178, 2018. 21 [RS18b] A. Reyes and Y. Suárez. On the ACCP in skew Poincaré-Birkhoff-Witt extensions. Beitr Algebra Geom., 59(4):625–643, 2018. II, 17 [RS19a] A. Reyes and H. Suárez. Radicals and Köthe’s conjecture for skew PBW extensions. Commun. Math. Stat., 2019. https://doi.org/10.1007/s40304-019-00189-0. 22 [RS19b] A. Reyes and H. Suárez. Skew Poincaré–Birkhoff–Witt extensions over weak zip rings. Beitr. Algebra Geom., 60(2):197–216, 2019. 14 [SLR17] H. Suárez, O. Lezama, and A. Reyes. Calabi-Yau property for graded skew PBW extensions. Rev. Colomb. Mat., 51(2):221–239, 2017. II, 14, 18 [SR17] H. Suárez and M. Reyes. A generalized Koszul property for skew PBW extensions. Far East J. Math. Sci. (FJMS), 101(2):301–320, 2017. 18 [SR19] H. Suárez and A. Reyes. Nakayama automorphism of some skew PBW extensions. Ingeniería y Ciencia, 15(29):157–177, 2019. 14 |
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Maximality of noncommutative rings over ordersRodríguez Rodríguez, Camilo AndrésMatemáticasOrderMaximal orderOre extensionPBW extensionSkew PBW extensionOre-Rees ringOrdenOrden maximalExtensión de OreExtensión PBWExtensión PBW torcidaAnillo de Ore-ReesLa teoría de órdenes ha sido ampliamente estudiada desde la última parte del siglo XX. En el contexto no conmutativo, la maximalidad de órdenes ha sido revisada para objetos clásicos de tipo polinomial como las extensiones de Ore y las extensiones PBW, entre otras, y más recientemente para anillos de Ore-Rees. En este trabajo extendemos algunos resultados encontrados en la literatura a las extensiones PBW torcidas.Order theory has been widely studied since the last part of the 20th century. In the noncommutative context, maximality of orders has been reviewed for classical objects of polynomial type such as Ore extensions and PBW extensions, among others, and more recently for Ore-Rees rings. In this work we extend some results found in the literature to skew PBW extensions.Magister en Ciencias MatemáticasMaestríaDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede BogotáReyes Villamil, Milton Armando2020-02-25T16:57:26Z2020-02-25T16:57:26Z2019-07-31Trabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_bdcchttp://purl.org/coar/version/c_ab4af688f83e57aaText48application/pdfapplication/pdfhttps://repositorio.unal.edu.co/handle/unal/75731eng[AAMAI11] A. Amir, P. Astuti, I. Muchtadi-Alamsyah, and I. Irawati. On maximal orders and factor rings of Ore extension over a commutative Dedekind domain. Far East J. Math. Sci., 55(1):21–30, 08 2011. 9 [AHK17] A. Alhevaz, E. Hashemi, and K. Khalilnezhad. (Σ,∆)-compatible skew PBW extension ring. Kyungpook Math. J, 57(3):401–417, 2017. 14 [AHK19] A. Alhevaz, E. Hashemi, and K. Khalilnezhad. Extensions of rings over 2-primal rings. Matematiche, LXXIV(I):141–162, 2019. 14 [AL15] J. P. Acosta and O. Lezama. Universal property of skew PBW extensions. Algebra Discrete Math., 20(1):1–12, 2015. 14 [AM03] E. Akalan and H. Marubayashi. Multiplicative ideal theory in noncommutative rings. Mathematical Notes, 74(3):401–410, 2003. 36 [Art15] V. A. Artamonov. Derivations of skew PBW extensions. Commun. Math. Stat., 3(4):449–457, 2015. 14 [BG88] A. Bell and K. Goodearl. Uniform rank over differential operator rings and PoincaréBirkhoff-Witt extensions. Pacific J. Math., 131(1):13–37, 1988. II, 1, 10, 11, 34 [CH80] A. W. Chatters and C. R. Hajarnavis. Rings with chain conditions. Chapman & Hall, 1980. 25 [Cha81] M. Chamarie. Anneaux de Krull noncommutatifs. J. Algebra, 72(1):210–222, 1981. 9, 27, 28 [Coh50] I. S. Cohen. Commutative rings with restricted minimum condition. Duke Math. J., 17(1):27–42, 1950. 26 [ER70] D. Eisenbud and J. C. Robson. Hereditary Noetherian prime rings. J. Algebra, 16:86– 104, 1970. 28, 36 [Faj19] W. Fajardo. A computational Maple library for skew PBW extensions. Fund. Inform., 167(3):159–191, 2019. 15 [GHK19] M. Ghadiri, E. Hashemi, and K. Khalilnezhad. Baer and quasi-Baer properties of skew PBW extensions. J. Algebr. Syst, 7(1):1–24, 2019. 14 [GL11] C. Gallego and O. Lezama. Gröbner bases for ideals of σ-PBW extensions. Comm. Algebra., 39(1):50–75, 2011. II, 14, 15 [GL16] C. Gallego and O. Lezama. d-Hermite rings and skew PBW extensions. São Paulo J. Math. Sci., 10(1):60–72, 2016. 14, 15 [GL17] C. Gallego and O. Lezama. Projective modules and Gröbner bases for skew PBW extensions. Dissertationes Math., 521:1–50, 2017. 15 [HHR19] M. Hamidizadeh, E. Hashemi, and A. Reyes. A classification of ring elements in skew PBW extensions over compatible rings. 2019. Submitted. 14 [HL72] C. R. Hajarnavis and T. Lenagan. Localisation in Asano Orders. J. Algebra, 21:441–449, 1972. 27 [HMU16] M. Helmi, H. Marubayashi, and A. Ueda. Ore-Rees rings which are maximal orders. J. Math. Soc. Japan, 68(1):405–423, 2016. II, III, 12, 13 [JL16] H Jiménez and O. Lezama. Gröbner bases for modules over σ-PBW extensions. Acta Math. Acad. Paedagog. Nyházi. (N.S.), 31(3):39–66, 2016. 15 [JR18] J. Jaramillo and A. Reyes. Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions. Ingeniería y Ciencia, 14(27):29–52, 2018. III, 16 [KMU85] Kazuo Kishimoto, Hidetoshi Marubayashi, and Akira Ueda. An Ore extension over a v-HC order. Math. J. Okayama Univ., 27:107–120, 1985. 23 [Kuz72] J. Kuzmanowich. Localizations of Dedekind prime rings. J. Algebra, 21(3):378–393, 1972. 27 [LAC+13] O. Lezama, J. P. Acosta, C. Chaparro, I. Ojeda, and C. Venegas. Ore and Goldie theorems for skew PBW extensions. Asian-European J. Math., 06(04):1350061, 2013. 24 [LAR15] O. Lezama, J. P. Acosta, and A. Reyes. Prime ideals of skew PBW extensions. Rev. Un. Mat. Argentina, 56(2):39–55, 2015. 14, 15, 22 [Lez16] O. Lezama. Cuadernos de Álgebra, No. 9: Álgebra no conmutativa, volume 123. SAC2, Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, 2016. http://sites.google.com/a/unal.edu.co/sac2. 29, 30, 31, 32, 33, 34, 35 [Lez19] O. Lezama. Computation of point modules of finitely semi-graded rings. Comm. Algebra, 2019. https://doi.org/10.1080/00927872.2019.1666404. 14 [LG19] O. Lezama and J. Gómez. Koszulity and point modules of finitely semi-graded rings and algebras. Symmetry, 11(7):1–22, 2019. 18 [LR11] L Levy and C. Robson. Hereditary Noetherian Prime Rings and Idealizers. American Mathematical Society, 2011. 9 [LR14] O. Lezama and A. Reyes. Some Homological Properties of Skew PBW Extensions. Comm. Algebra, 42(3):1200–1230, 2014. II, 14, 16, 17, 18, 19, 20, 22 [LRS15] O. Lezama, A. Reyes, and H. Suárez. Some relations between N-Koszul, ArtinSchelter Regular and Calabi-Yau algebras with skew PBW extensions. Ciencia en Desarrollo, 6(2):205–213, 2015. 16, 18 [LV17] O. Lezama and H. Venegas. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry. Discuss. Math. Gen. Algebra Appl, 37(1):45–57, 2017. 14 [Mar80] H. Marubayashi. Polynomial rings over Krull orders in simple Artinian rings. Hokkaido Math. J., 9:63–78, 1980. 27 [Mar83] H. Marubayashi. A Krull type generalization of HNP rings with enough invertible ideals. Comm. Algebra, 11(5):469–499, 1983. 25, 27, 28 [Mar84] H. Marubayashi. A skew polynomial ring over a v-HC order with enough v-invertible ideals. Comm. Algebra, 12(13):1567–1593, 1984. 24 [McC74] J. McConnell. Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture. Proc. London Math. Soc., s3-29:453–484, 1974. 10 [Mic69] G. O. Michler. Asano orders. Proc. London Math. Soc., 3:421–423, 1969. 27 [MR01] J. McConnell and J. Robson. Noncommutative Noetherian Rings. American Mathematical Society, 2001. II, 1, 2, 3, 4, 5, 6, 7, 8, 9, 32, 33, 35 [MU17] H. Marubayashi and A. Ueda. Examples of Ore extensions which are maximal orders whose based rings are not maximal orders. J. Algebra, 479:368–379, 2017. II, III, 9, 10 [MYZ98] H. Marubayashi, P. Yang, and Y Zhang. Some examples of PBW extensions which are Krull orders. Math. Japonica, 1998. 36 [MZ96] H. Marubayashi and Y. Zhang. Maximality of PBW extensions of orders. Comm. Algebra, 24(4):1377–1388, 1996. II, III, 10, 11, 21, 22, 23, 24, 25, 26, 28 [NR17] A. Niño and A. Reyes. Some ring theoretical properties of skew Poincaré-BirkhoffWitt extensions. Bol. Mat., 24(2):131–148, 2017. 14, 21 [Ore33] O. Ore. Theory of Non-Commutative Polynomials. Ann. of Math., 34(3):480–508, 1933. II, 8 [Pas87] D. S. Passman. Prime ideals in enveloping rings. Trans. Amer. Math. Soc, 302(2):535– 560, 1987. 11, 17 [Rey13] A. Reyes. Ring and Module Theoretical Properties of skew PBW extensions. PhD thesis, Universidad Nacional de Colombia, Bogotá., 2013. II, 16, 18 [Rey14] A. Reyes. Uniform dimension over skew PBW extensions. Rev. Col. Mat., 48(1):79–96, 2014. 16, 34 [Rey15] A. Reyes. Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings. Rev. Integr. Temas Mat., 33(2):173–189, 2015. 17, 19 [Rin63] G. S. Rinehart. Differential forms on general commutative algebras. Trans. Amer. Math. Soc., 108(2):195–222, 1963. 10 [RR19] A. Reyes and C. Rodríguez. The McCoy condition on Skew Poincaré-Birkhoff-Witt Extensions. Commun. Math. Stat, 2019. https://doi.org/10.1007/s40304-019-00184-5. 14 [RS16a] A. Reyes and H. Suárez. Armendariz property for skew PBW extensions and their classical ring of quotients. Rev. Integr. Temas Mat, 34(2):147–168, 2016. 21 [RS16b] A. Reyes and H. Suárez. A Note on Zip and reversible skew PBW extensions. Bol. Mat, 23(1):71–79, 2016. 14 [RS16c] A. Reyes and H. Suárez. Some remarks about the cyclic homology of skew PBW extensions. Ciencia en Desarrollo, 7(2):99–107, 2016. 14 [RS17a] A. Reyes and H. Suárez. Bases for quantum algebras and skew Poincaré-BirkhoffWitt extensions. 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Skew Poincaré–Birkhoff–Witt extensions over weak zip rings. Beitr. Algebra Geom., 60(2):197–216, 2019. 14 [SLR17] H. Suárez, O. Lezama, and A. Reyes. Calabi-Yau property for graded skew PBW extensions. Rev. Colomb. Mat., 51(2):221–239, 2017. II, 14, 18 [SR17] H. Suárez and M. Reyes. A generalized Koszul property for skew PBW extensions. Far East J. Math. Sci. (FJMS), 101(2):301–320, 2017. 18 [SR19] H. Suárez and A. Reyes. Nakayama automorphism of some skew PBW extensions. Ingeniería y Ciencia, 15(29):157–177, 2019. 14Derechos reservados - Universidad Nacional de ColombiaAtribución-NoComercial 4.0 InternacionalAcceso abiertohttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessreponame:Repositorio UNinstname:Universidad Nacional de Colombiainstacron:Universidad Nacional de Colombia2025-01-07T16:15:16Z |
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