Relative coherent modules

TL;DR

This paper introduces the concept of coherent-like modules to unify various existing relative coherent ring concepts, generalizing classical results and providing new insights into their structure.

Contribution

It extends the unification of coherent-like rings to modules, offering a broader framework and new results in the theory of relative coherent modules.

Findings

Unified various relative coherent concepts through modules

Generalized classical results in coherent module theory

Introduced new results in the structure of coherent-like modules

Abstract

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like rings are unified. In this manuscript we continue this work and we introduce coherent-like module which also emphasizes our point of view by unifying the existed relative coherent concepts. Several classical results are generalized and some new results are given.