COMMUTATIVE DIAGRAMS OF EXACT SEQUENCES OF S-ACTS BASED ON CONGRUENCES

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Faculty of Sciences, Fasa University, Fasa, Iran.

2 College of Engineering, Lamerd Higher Education Center, Shiraz University of Technology, Lamerd, Iran.

3 Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

10.22044/jas.2025.15052.1894

Abstract

In the theory of S-acts, congruences are not generally defined by subacts. However, as factor acts are defined by congruences, the congruences are of as great importance in the theory of S-acts. This paper focuses on studying the generalized notion of
a (short) exact sequence for S-acts with respect to a congruence. The behavior of chain conditions for these sequences is examined.
The main purpose of this paper is to investigate commutative diagrams of these generalized exact sequences. Finally, we generalize
the Snake Lemma for S-acts.

Keywords

References

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Journal of Algebraic Systems
Volume 14, Issue 4
September 2026
Pages 671-681

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