Publication:
π-endo Baer modules

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Date

2020-03-03

Authors

Birkenmeier, Gary F.
Kara, Yeliz
Tercan, Adnan

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Taylor & Francis

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Abstract

Let N be a submodule of a right R-module M-R, and Then N is said to be projection invariant in M, denoted by if for all We call M-R ?-endo Baer, denoted ?-e.Baer, if for each there exists such that where denotes the left annihilator of N in H. We show that this class of modules lies strictly between the classes of Baer and quasi-Baer modules introduced in 2004 by Rizvi and Roman. Several structural properties are developed. In contrast to the Baer modules of Rizvi and Roman, the free modules of a Baer ring are ?-e.Baer. Moreover, (co-) nonsingularity conditions are introduced which enable us to extend the Chatters-Khuri result (connecting the extending and Baer conditions in a ring) to modules. We provide examples to illustrate and delimit our results.

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Keywords

Direct sums, Invariant, Submodules, Rings, Baer module, Endomorphism rings, Projection invariant submodule, Quasi-baer module, Pi-extending module, Pi-e.Baer module, Mathematics

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