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 $n$ - $𝒳$ -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.

Communicated by A. R. Rajan

Keywords:

AMSC: 16D80, 16E05, 16E30, 16E65, 16P70

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