Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(2): 347-358

Online first article December 27, 2021      Printed April 30, 2022

https://doi.org/10.4134/CKMS.c210114

Copyright © The Korean Mathematical Society.

Co-uniform and hollow $S$-acts over monoids

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

MSC numbers: 20M30

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