Co-uniform and hollow S-acts over monoids
Commun. Korean Math. Soc.
Published online December 27, 2021
Roghaieh Khosravi and 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 subact, 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-act.
Keywords : monoids . S-acts . superfluous . coessential . hollow
MSC numbers : 20M30
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