Matlis duality, inverse systems and classification of Artin algebras

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Joan Elías García

Detalles Bibliográficos
Autor: Sánchez Ruiz, Noelia
Tipo de recurso: tesis de maestría
Fecha de publicación:2023
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/202200
Acceso en línea:https://hdl.handle.net/2445/202200
Access Level:acceso abierto
Palabra clave:Anells (Àlgebra)
Àlgebra commutativa
Treballs de fi de màster
Anells locals
Rings (Algebra)
Commutative algebra
Master's thesis
Local rings
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spelling Matlis duality, inverse systems and classification of Artin algebrasSánchez Ruiz, NoeliaAnells (Àlgebra)Àlgebra commutativaTreballs de fi de màsterAnells localsRings (Algebra)Commutative algebraMaster's thesisLocal ringsTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Joan Elías García[en] The aim of this project is to study the classification of some families of Artin algebras. In order to do that, we will study some important results of injective modules with the objective to be able to prove Matlis duality. In particular, we will study the case of Matlis duality when $R=\mathbf{k} \llbracket x_1, \ldots, x_n \rrbracket$ (the ring of the formal series) with maximal ideal $\mathfrak{m}=\left(x_1, \ldots, x_n\right)$. With this scenario, we are talking about Macaulay's duality. Using Macaulay's correspondence, we will be able to study important results as Hilbert functions, essential in the classification of algebras. We will study Gorenstein, level and compressed algebras. Along the paper, we use Singular [DGPS22] and the library Inverse SYST.LIB by Joan Elias [Eli14], which with we will compute some examples seen through the project.Elías García, Joan2023info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/202200Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Noelia Sánchez Ruiz, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2022002026-05-27T06:46:51Z
dc.title.none.fl_str_mv Matlis duality, inverse systems and classification of Artin algebras
title Matlis duality, inverse systems and classification of Artin algebras
spellingShingle Matlis duality, inverse systems and classification of Artin algebras
Sánchez Ruiz, Noelia
Anells (Àlgebra)
Àlgebra commutativa
Treballs de fi de màster
Anells locals
Rings (Algebra)
Commutative algebra
Master's thesis
Local rings
title_short Matlis duality, inverse systems and classification of Artin algebras
title_full Matlis duality, inverse systems and classification of Artin algebras
title_fullStr Matlis duality, inverse systems and classification of Artin algebras
title_full_unstemmed Matlis duality, inverse systems and classification of Artin algebras
title_sort Matlis duality, inverse systems and classification of Artin algebras
dc.creator.none.fl_str_mv Sánchez Ruiz, Noelia
author Sánchez Ruiz, Noelia
author_facet Sánchez Ruiz, Noelia
author_role author
dc.contributor.none.fl_str_mv Elías García, Joan
dc.subject.none.fl_str_mv Anells (Àlgebra)
Àlgebra commutativa
Treballs de fi de màster
Anells locals
Rings (Algebra)
Commutative algebra
Master's thesis
Local rings
topic Anells (Àlgebra)
Àlgebra commutativa
Treballs de fi de màster
Anells locals
Rings (Algebra)
Commutative algebra
Master's thesis
Local rings
description Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Joan Elías García
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/202200
url https://hdl.handle.net/2445/202200
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-nd (c) Noelia Sánchez Ruiz, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Noelia Sánchez Ruiz, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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