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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Auslander-Reiten conjecture for Gorenstein rings


Author: Tokuji Araya
Journal: Proc. Amer. Math. Soc. 137 (2009), 1941-1944
MSC (2000): Primary 13H10, 13D02, 13D07
Published electronically: December 17, 2008
MathSciNet review: 2480274
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Abstract: The Nakayama conjecture is one of the most important conjectures in ring theory. The Auslander-Reiten conjecture is closely related to it. The purpose of this paper is to show that if the Auslander-Reiten conjecture holds in codimension one for a commutative Gorenstein ring $ R$, then it holds for $ R$.


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Additional Information

Tokuji Araya
Affiliation: Nara University of Education, Takabatake-cho, Nara City 630-8528, Japan
Email: araya@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09757-8
PII: S 0002-9939(08)09757-8
Keywords: Auslander-Reiten conjecture, Gorenstein ring, stable cohomology module
Received by editor(s): April 28, 2008
Received by editor(s) in revised form: August 25, 2008
Published electronically: December 17, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.