Two generalizations of homology modules

Abstract

Let R be a commutative ring and Nil(R) denote the set of nilpotent elements of R. In this paper, we investigate two generalizations of exact sequences, ϕ -exact sequences and N -exact sequences. With the help of two generalizations of exact sequences, we generalize the concept of homology modules. We show that they behave in a way similar to the classical ones.