## Complete pure injectivity and endomorphism rings

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- by J. L. Gómez Pardo, Nguyen V. Dung and R. Wisbauer PDF
- Proc. Amer. Math. Soc.
**118**(1993), 1029-1034 Request permission

## 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.## References

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## Additional Information

- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**118**(1993), 1029-1034 - MSC: Primary 16D50; Secondary 16D90, 16S50, 18E15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1137232-X
- MathSciNet review: 1137232