Co-uniform and hollow $S$-acts over monoids
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 347-358
Published online December 27, 2021
Printed April 30, 2022
Roghaieh Khosravi, Mohammad Roueentan
Fasa University; Lamerd Higher Education Center
Abstract : In this paper, we first introduce the notions of superfluous and coessential subacts. Then hollow and co-uniform $S$-acts are defined as the acts that all proper subacts are superfluous and coessential, respectively. Also it is indicated that the class of hollow $S$-acts is properly between two classes of indecomposable and locally cyclic $S$-acts. Moreover, using the notion of radical of an $S$-act as the intersection of all maximal subacts, the relations between hollow and local $S$-acts are investigated. Ultimately, the notion of a supplement of a subact is defined to characterize the union of hollow $S$-acts.
Keywords : Monoids, $S$-acts, superfluous, coessential, hollow
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