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

 

Complete pure injectivity and endomorphism rings


Authors: J. L. Gómez Pardo, Nguyen V. Dung and R. Wisbauer
Journal: Proc. Amer. Math. Soc. 118 (1993), 1029-1034
MSC: Primary 16D50; Secondary 16D90, 16S50, 18E15
MathSciNet review: 1137232
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Abstract: It is shown that if $ M$ is a finitely presented completely pure injective object in a locally finitely generated Grothendieck category $ {\mathbf{C}}$ such that $ S = {\operatorname{End} _{\mathbf{C}}}M$ is von Neumann regular, then $ S$ is semisimple. This is a generalized version of a well-known theorem of Osofsky, which includes also a result of Damiano on PCI-rings. As an application, we obtain a characterization of right hereditary rings with finitely presented injective hull.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1137232-X
PII: S 0002-9939(1993)1137232-X
Article copyright: © Copyright 1993 American Mathematical Society