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

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.

Keywords:

(Rees) Noetherian , (Rees) Artinian , composition series