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Characterizing Topologically Dense Injective Acts and Their Monoid Connections

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  • Masoomeh Hezarjaribi Dastaki
  • Hamid Rasouli
  • Hasan Barzegar
  • G. Muhiuddin

Abstract

In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free S-act over a monoid S is topologically dense injective if and only if S is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.

Suggested Citation

  • Masoomeh Hezarjaribi Dastaki & Hamid Rasouli & Hasan Barzegar & G. Muhiuddin, 2024. "Characterizing Topologically Dense Injective Acts and Their Monoid Connections," Journal of Mathematics, Hindawi, vol. 2024, pages 1-11, May.
    • Handle: RePEc:hin:jjmath:2966461
    DOI: 10.1155/2024/2966461
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