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, $\varphi$-exact sequences and $\text{N}$-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.

KEYWORDS:

• $\varphi$-exact sequence
• nonnil-commutative diagram
• nonnil-homology module
• weakly nonnil-homology module

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13C05
• 13C10
• 13C12

Additional information

Funding

This document is the results of the research project funded by the National Natural Science Foundation of China 12061001, the China Postdoctoral Science Foundation 2021M691526, the Science and Technology Plan Project in Sichuan Province 2023NSFSC0074, and Aba teachers university AS-HBZ2023-34, AS-HBZ2023-35, 20210103002, 20210403010, 20210406032.