Algebras with radical square zero are either self-injective or CM-free

By Xiao-Wu Chen. 2011

57 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8bbd072bd1f63883c2f5213577bce226cc173bc4

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Citations in the corpus

The Gorenstein projective modules for the Nakayama algebras. I (2012, background): “Chen. Algebras with radical square zero are either self-injective or CM-free. Proc. Amer. Math. Soc. 140 (2012), 93-98.”
The singularity category of an algebra with radical square zero (2011, background): “We point out that such algebras are usually non-Gorenstein ([5]).”
The Gorenstein-projective modules over a monomial algebra (2015, background): “(2) The algebra A is CM-free if and only if the relation quiver RA contains no perfect component.”