Starting with some observations on (strong) lifting of idempotents, we characterize a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with small image. This is the dual of Yamagata's work [Colloq. Math. 113 (2008)] on a module whose endomorphism ring is semiregular with respect to the ideal of endomorphisms with large kernel.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-7,
author = {Tsiu-Kwen Lee and Yiqiang Zhou},
title = {On lifting of idempotents and semiregular endomorphism rings},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {99-113},
zbl = {1277.16018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-7}
}
Tsiu-Kwen Lee; Yiqiang Zhou. On lifting of idempotents and semiregular endomorphism rings. Colloquium Mathematicae, Tome 122 (2011) pp. 99-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-7/