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On PP-Endomorphism Rings

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson
W. K. Nicholson*
Affiliation:
Department of Mathematics and Statistics University of Calgary T2N 1N4
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Abstract

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A characterization is given of when all kernels (respectively images) of endomorphisms of a module are direct summands, a necessary condition being that the endomorphism ring itself is a left (respectively right) PP-ring. This result generalizes theorems of Small, Lenzing and Colby-Rutter and shows that R is left hereditary if and only if the endomorphism ring of every injective left module is a right PP-ring.

Keywords

16A65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 227 - 230
Copyright
Copyright © Canadian Mathematical Society 1993

References

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5. Zelmanowitz, J. M., Regular modules, Trans. A.M.S. 163(1972), 341–355.Google Scholar