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On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions

  Published:2014-11-03
 Printed: Mar 2015
  • Saeed Nasseh,
    Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA
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Abstract

We show under some conditions that a Gorenstein ring $R$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does $R[x]$. 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 Auslander-Reiten conjecture, finitistic extension degree, Gorenstein rings
MSC Classifications: 13D07, 16E30, 16E65 show english descriptions Homological functors on modules (Tor, Ext, etc.)
Homological functors on modules (Tor, Ext, etc.)
Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
13D07 - Homological functors on modules (Tor, Ext, etc.)
16E30 - Homological functors on modules (Tor, Ext, etc.)
16E65 - Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
 

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