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arXiv · 1803.01827

On reflexive simple modules in Artin algebras

Rene Marczinzik
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Abstract

Let $A$ be an Artin algebra. It is well known that $A$ is selfinjective if and only if every finitely generated $A$-module is reflexive. In this article we pose and motivate the question whether an algebra $A$ is selfinjective if and only if every simple module is reflexive. We give a positive answer to this question for large classes of algebras which include for example all Gorenstein algebras and all QF-3 algebras.

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Rene Marczinzik. 2018-03-05. On reflexive simple modules in Artin algebras. https://arxiv.org/abs/1803.01827

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