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Some Properties of Grey S-Acts Over Monoids

Author

Listed:
  • Masoomeh Hezarjaribi

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

  • Zohreh Habibi

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

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, Act0 − GS. 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.

Suggested Citation

  • Masoomeh Hezarjaribi & Zohreh Habibi, 2022. "Some Properties of Grey S-Acts Over Monoids," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 313-323, July.
    • Handle: RePEc:wsi:nmncxx:v:18:y:2022:i:02:n:s1793005722500168
    DOI: 10.1142/S1793005722500168
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