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Primitive submodules, co-semisimple and regular modules. (English) Zbl 1398.16004

Summary: In this paper, primitive submodules are defined and various properties of them are investigated. Some characterizations of co-semisimple modules are given and several conditions under which co-semisimple and regular modules coincide are discussed.

MSC:

16D40 Free, projective, and flat modules and ideals in associative algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16D90 Module categories in associative algebras
16P20 Artinian rings and modules (associative rings and algebras)
16D80 Other classes of modules and ideals in associative algebras
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