Characterizations of regular modules

Anahtar Kelimeler:

Regular module, reduced module, (weakly-)morphic module

Characterizations of regular modules

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations of these distinct notions for modules in terms of both (weakly-)morphic modules and reduced modules. Furthermore, module theoretic settings are established where these in general distinct notions turn out to be indistinguishable.

Keywords:

Regular module, reduced module, (weakly-)morphic module,

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