Quasidualizing modules

Bethany Kubik

doi:10.1216/JCA-2014-6-2-209

Quasidualizing modules

Bethany Kubik

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We introduce and study "quasidualizing" modules. An artinian R-module T is quasidualizing if the homothety map Rˆ → Hom_R(T,T) is an isomorphism and Extⁱ_R(T,T) = 0 for each integer i > 0. Quasidualizing modules are associated to semidualizing modules via Matlis duality. We investigate the associations via Matlis duality between subclasses of the Auslander class and Bass class and subclasses of derived T-reflexive modules.

Original language	English (US)
Pages (from-to)	209-229
Number of pages	21
Journal	Journal of Commutative Algebra
Volume	6
Issue number	2
DOIs	https://doi.org/10.1216/JCA-2014-6-2-209
State	Published - 2014

Bibliographical note

Publisher Copyright:
© 2014 Rocky Mountain Mathematics Consortium.

Keywords

Artinian
Hom
Matlis duality
Noetherian
Quasidualizing
Semidualizing
Tensor product

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10.1216/JCA-2014-6-2-209

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keywords = "Artinian, Hom, Matlis duality, Noetherian, Quasidualizing, Semidualizing, Tensor product",

author = "Bethany Kubik",

note = "Publisher Copyright: {\textcopyright} 2014 Rocky Mountain Mathematics Consortium.",

year = "2014",

doi = "10.1216/JCA-2014-6-2-209",

language = "English (US)",

volume = "6",

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AB - We introduce and study "quasidualizing" modules. An artinian R-module T is quasidualizing if the homothety map Rˆ → HomR(T,T) is an isomorphism and ExtiR(T,T) = 0 for each integer i > 0. Quasidualizing modules are associated to semidualizing modules via Matlis duality. We investigate the associations via Matlis duality between subclasses of the Auslander class and Bass class and subclasses of derived T-reflexive modules.

KW - Artinian

KW - Hom

KW - Matlis duality

KW - Noetherian

KW - Quasidualizing

KW - Semidualizing

KW - Tensor product

UR - https://www.scopus.com/pages/publications/84907062990

UR - https://www.scopus.com/inward/citedby.url?scp=84907062990&partnerID=8YFLogxK

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DO - 10.1216/JCA-2014-6-2-209

M3 - Article

AN - SCOPUS:84907062990

SN - 1939-0807

VL - 6

SP - 209

EP - 229

JO - Journal of Commutative Algebra

JF - Journal of Commutative Algebra

IS - 2

ER -

Quasidualizing modules

Abstract

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Keywords

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