Cogenerator endomorphism rings
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- by Ronald L. Wagoner PDF
- Proc. Amer. Math. Soc. 28 (1971), 347-351 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- 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