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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Cogenerator endomorphism rings


Author: Ronald L. Wagoner
Journal: Proc. Amer. Math. Soc. 28 (1971), 347-351
MSC: Primary 16.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0276267-1
MathSciNet review: 0276267
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Abstract: If $ R$ is a ring and $ P$ is a finitely generated projective right $ R$-module, what properties of $ R$ does the $ R$-endomorphism ring of $ P$ inherit? Rosenberg and Zelinsky have shown that if $ R$ is quasi-Frobenius, and $ P$ also has every simple epimorphic image isomorphic to a submodule, then the $ R$-endomorphism ring of $ P$ is also quasi-Frobenius. In this paper we show that if $ R$ is a cogenerator ring, and $ P$ is a finitely generated projective right $ R$-module with every simple epimorphic image isomorphic to a submodule of $ P$, then the $ R$-endomorphism ring of $ P$ is also a cogenerator ring.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276267-1
Keywords: Injective cogenerator, injective envelope, endomorphism ring, congenerator ring, basic idempotent, finitely generated projective module
Article copyright: © Copyright 1971 American Mathematical Society

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