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Algebras with radical square zero are either self-injective or CM-free
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Journal Article
Algebras with radical square zero are either self-injective or CM-free
2012
Overview
An artin algebra is called CM-free provided that all its finitely generated Gorenstein projective modules are projective. We show that a connected artin algebra with radical square zero is either self-injective or CM-free. As a consequence, we prove that a connected artin algebra with radical square zero is Gorenstein if and only if its valued quiver is either an oriented cycle with the trivial valuation or does not contain oriented cycles.
Publisher
American Mathematical Society
Subject
