On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions

Saeed Nasseh

doi:10.4153/CMB-2014-052-9

On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions

Saeed Nasseh

Mathematical Sciences

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

Abstract

We show that under some conditions a Gorenstein ring R satisfies the Generalized Auslander-Reiten conjecture if and only if R[x] does. When R is a local ring we prove the same result for some localizations of R[x].

Original language	American English
Journal	Canadian Mathematical Bulletin
Volume	58
DOIs	https://doi.org/10.4153/CMB-2014-052-9
State	Published - Mar 1 2015

Keywords

Auslander-Reiten conjecture
Finitistic extension degree
Gorenstein rings

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Education
Mathematics

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http://dx.doi.org/10.4153/CMB-2014-052-9

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title = "On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions",

abstract = "We show that under some conditions a Gorenstein ring R satisfies the Generalized Auslander-Reiten conjecture if and only if R[x] does. When R is a local ring we prove the same result for some localizations of R[x].",

keywords = "Auslander-Reiten conjecture, Finitistic extension degree, Gorenstein rings",

author = "Saeed Nasseh",

note = "Publisher Copyright: Copyright {\textcopyright} 2014 Canadian Mathematical Society.",

year = "2015",

month = mar,

day = "1",

doi = "10.4153/CMB-2014-052-9",

language = "American English",

volume = "58",

journal = "Canadian Mathematical Bulletin",

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N2 - We show that under some conditions a Gorenstein ring R satisfies the Generalized Auslander-Reiten conjecture if and only if R[x] does. When R is a local ring we prove the same result for some localizations of R[x].

AB - We show that under some conditions a Gorenstein ring R satisfies the Generalized Auslander-Reiten conjecture if and only if R[x] does. When R is a local ring we prove the same result for some localizations of R[x].

KW - Auslander-Reiten conjecture

KW - Finitistic extension degree

KW - Gorenstein rings

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/289

UR - http://dx.doi.org/10.4153/CMB-2014-052-9

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DO - 10.4153/CMB-2014-052-9

M3 - Article

SN - 0008-4395

VL - 58

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

ER -

On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions

Abstract

Keywords

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