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On the Generalized Auslander–Reiten Conjecture under Certain Ring Extensions

Published online by Cambridge University Press:  20 November 2018

Saeed Nasseh
Saeed Nasseh*
Affiliation:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA. e-mail: snasseh@georgiasouthern.edu
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Abstract

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

Keywords

13D0716E3016E65Auslander–Reiten conjecturefinitistic extension degreeGorenstein rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 134 - 143
Copyright
Copyright © Canadian Mathematical Society 2015

References

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