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Endomorphism Ring of GZ-Regular Modules | ||
| Diyala Journal For Pure Science | ||
| Article 1, Volume 12, Issue 3, 2016, Pages 79-93 | ||
| Author | ||
| Areej M. Abduldaim | ||
| Abstract | ||
| As a complement to the former work of GZ-regular modules, in this paper along the lines of Z-regular modules due to Zelmanowitz, we improve the study of the endomorphism ring of Z-regular modules to GZ-regular modules. We give a sufficient condition on GZ-regular module M such that S=End(M) is π-regular ring and we prove that R-module M is GZ-regular if and only if S=End(M) is π-regular ring in case that M is a projective finitely power generated R-module. Also we show that for a GZ-regular R-module M, the center of S=End(M), Cen(S), is π-regular ring. Even further if M is a GZ-regular R-module then R/ann(M) is dense in Cen(S). | ||
| Keywords | ||
| endomorphism ring; regular module; regular ring; projective module | ||
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