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A NOTE ON FULLY IDEMPOTENT S-ACTS
Roueentan, Mohammad,Ershad, Majid The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.3
In this article we introduce the notion of fully idempotent acts and by this we give a characterization of commutative monoids over which all cyclic right acts are injective.
A NOTE ON FULLY IDEMPOTENT S-ACTS
( Mohamad Roueentan ),( Majid Ershad ) 호남수학회 2013 호남수학학술지 Vol.35 No.3
In this article we introduce the notion of fully idempotent acts and by this we give a characterization of commutative monoids over which all cyclic right acts are injective.
CO-UNIFORM AND HOLLOW S-ACTS OVER MONOIDS
Khosravi, Roghaieh,Roueentan, Mohammad Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
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.
ON DIFFERENT KINDS OF INJECTIVITY OF ACTS
Naghipoor, Mohammad Ali,Ershad, Majid,Roueentan, Mohammad The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.3
In this paper we introduce some new kinds of injectivities, namely, LC (resp. Ind, PInd) injectivity and investigate the relation among various kinds of injectivities. Some classifications of monoids by properties of these kinds of injective acts are presented. Among other results, it is shown that over a principal right ideal monoid, right completely LC-injectivity implies right completely injectivity. Also over a monoid with a zero Ind-injective (resp. PInd-injective) acts are injective.
ON DIFFERENT KINDS OF INJECTIVITY OF ACTS
( Mohammad Ali Naghipoor ),( Majid Ershad ),( Mohammad Roueentan ) 호남수학회 2017 호남수학학술지 Vol.39 No.3
In this paper we introduce some new kinds of injectivities, namely, LC (resp. Ind, PInd) injectivity and investigate the relation among various kinds of injectivities. Some classi_cations of monoids by properties of these kinds of injective acts are presented. Among other results, it is shown that over a principal right ideal monoid, right completely LC-injectivity implies right completely injectivity. Also over a monoid with a zero Ind-injective (resp. PInd-injective) acts are injective.