Relative coherent modules

Abstract

Several authors have introduced various types 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 [Formula: see text]-[Formula: see text]-coherent rings, Int. Electron. J. Algebra, 7 (2010) 128–139, several coherent-like rings are unified. In this paper, 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.