Composition series on (Rees) congruences of S-acts.

Document Type : Research Paper

Authors

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

2 College of Engineering, Lamerd Higher Education Center, Lamerd, Iran.

Abstract

In this paper, we study composition series of subacts or congruences of S-acts. It is shown that composition series of subacts are exactly those that are both Rees artinian and Rees noetherian, i.e. those satisfying both ascending and descending chain conditions on subacts. But this is not valid for the case of composition series of congruences in general. We prove that the properties of having composition series of subacts or congruences are inherited in Rees short exact sequences. Also, we discuss whenever two composition series of subacts or congruences have the same length and they are equivalent.

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References

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Categories and General Algebraic Structures with Applications
Volume 19, Issue 1
August 2023
Pages 29-46

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