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Some Properties of Grey S-Acts Over Monoids

Masoomeh Hezarjaribi

Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran

E-mail Address: Masoomeh.hezarjaribi@pnu.ac.ir

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Zohreh Habibi

Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran

E-mail Address: Z_habibi@pnu.ac.ir

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https://doi.org/10.1142/S1793005722500168Cited by:0 (Source: Crossref)

Abstract

In this paper, we introduce the concept of grey S-acts and morphisms between grey S-acts on monoids, which construct a category, namely, $A c t_{0} - G S$ . Next, we define indecomposable, cyclic, free and projective grey S-acts. We show that any grey S-act is a free grey S-act if and only if it is a free object in this category. Also, we show that any grey S-act is epimorphism image of any free grey S-act. We prove that any free grey S-act is a projective grey S-act and any cyclic grey S-act is an indecomposable grey S-act.

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Vol. 18, No. 02

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Some Properties of Grey S-Acts Over Monoids

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