Purely Baer modules and purely Rickart modules

S. Ebrahimi Atani; M. Khoramdel; S. Dolati Pishhesari;


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

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