MMN-1484
Purely Baer modules and purely Rickart modules
S. Ebrahimi Atani; M. Khoramdel; S. Dolati Pishhesari;Abstract
We introduce the notions of purely Baer and purely Rickart
modules. We provide several characterizations and investigate properties of each of these concepts. We provide new characterizations of several well-known classes of rings in terms of purely Baer and purely Rickart modules.
It is shown that R is a von Numann regular ring iff every right R-module is purely Baer (purely Rickart). Also, we prove R is left semihereditary iff every (finitely generated) free right R-module is purely Baer. Examples illustrating the results are presented.
Vol. 19 (2018), No. 1, pp. 63-76
DOI: 10.18514/MMN.2018.1484