Co-uniform and hollow $S$-acts over monoids
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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.
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.
참고문헌 (10)
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