Grigore Calugareanu and Lavinia Pop: Morphic objects in categories, p.173-180

Abstract:

An $R$-module $_{R}M$ is called morphic if $M/{\rm im}\alpha \cong \ker \alpha$ for every endomorphism $\alpha$ of $M$, that is, if the dual of the Noether isomorphism theorem holds.

In this paper we consider this notion in categories with kernels and images and recover most of its properties under suitable conditions. Connection with unit-regular and regular objects is made.

Key Words: Morphic; p-exact; abelian; category; unit-regular.

2000 Mathematics Subject Classification: Primary: 18E10;
Secondary: 18A20.

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