Characterizations of regular modules

Year 2023, Volume: 33 Issue: 33, 54 - 76, 09.01.2023

Philly Ivan Kimuli David Ssevviiri

https://doi.org/10.24330/ieja.1224782

Abstract

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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