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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Xiao-Wu Chen
Journal: Proc. Amer. Math. Soc. 140 (2012), 93-98
MSC (2010): Primary 18G25, 16G10, 16G50
Published electronically: May 16, 2011
MathSciNet review: 2833520
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Abstract: 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.


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Additional Information

Xiao-Wu Chen
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, Anhui, People’s Republic of China
Email: xwchen@mail.ustc.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10921-3
PII: S 0002-9939(2011)10921-3
Received by editor(s): June 10, 2010
Received by editor(s) in revised form: November 9, 2010
Published electronically: May 16, 2011
Additional Notes: The author is supported by the Special Foundation of the President of the Chinese Academy of Sciences (No. 1731112304061) and by the National Natural Science Foundation of China (No. 10971206).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.