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Modules characterized by their simple submodules. (English) Zbl 1241.16002
The author investigates two known types of modules characterized by their simple submodules. Thus, a module is called PS (resp., FS) if every submodule is projective (resp., flat). Also, it is introduced and studied the concept of min-coherent module, defined as a module with every simple submodule finitely presented. Some closure properties are discussed and several characterizations are given.

MSC:
16D50 Injective modules, self-injective associative rings
16D40 Free, projective, and flat modules and ideals in associative algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)
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