Some remarks about the fusible property of noncommutative polynomial extensions
In this work, we focus on three objectives: first, we investigate fusible property on skew PBW extensions, recognizing conditions that guarantee the property for this family of algebras. Later, we turn our attention to the study of two very important ring families: the weak $\Sigma$-rigid rings defi...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/78465 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/78465 |
| Access Level: | acceso abierto |
| Palabra clave: | 510 - Matemáticas Fusible property Skew PBW extension Weak Σ-rigid ring (Σ,∆)-compatible ring Unit Nilpotent Zero divisor Idempotent Weak annihilator Associated prime ideal Propiedad fusible Extensión PBW torcida Anillo débil Σ-rígido Anillo (Σ,∆)-compatible Unidad Nilpotente Divisor de cero Idempotente Anulador débil Ideal primo asociado |
| Sumario: | In this work, we focus on three objectives: first, we investigate fusible property on skew PBW extensions, recognizing conditions that guarantee the property for this family of algebras. Later, we turn our attention to the study of two very important ring families: the weak $\Sigma$-rigid rings defined by Reyes et al., [2018] and $(\Sigma, \Delta)$-compatible rings introduced by Hashemi et al., [2017] and Reyes et al., [2018], respectively. We establish several results that characterize some important elements such as units, nilpotents, idempotents and zero divisors in skew PBW extensions over $(\Sigma, \Delta)$-compatible rings. We extend some descriptions of these elements for skew polynomial rings presented by Hashemi et al., [2017]. The study of these elements leads us to find a more general notion of annihilator, for which we investigate analogous properties to those that define the Baer, quasi-Baer, p.p and p.q.-Baer rings, extending some results presented by Ouyang et al., [2012]. Finally, having in mind a more general concept of associated prime ideal presented by Ouyang et al., [2012], we study this generalization of the associated primes and eventually characterize these ideals in skew PBW extensions over $(\Sigma, \Delta)$-compatible rings. |
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