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The Auslander-Reiten conjecture for Gorenstein rings

Author(s): Tokuji Araya
Journal: Proc. Amer. Math. Soc. 137 (2009), 1941-1944.
MSC (2000): Primary 13H10, 13D02, 13D07
Posted: December 17, 2008
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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: 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
Posted: December 17, 2008
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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