On Some Kinds of Injectivity of GHS-Acts

Authors

  • Maedeh Ghasempour Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
  • Hamid Rasouli Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
  • Ali Iranmanesh Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
  • Hasan Barzegar Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran
  • Abolfazl Tehranian Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

DOI:

https://doi.org/10.30495/jme.v18i0.2977

Keywords:

hypermonoid, generalized hyper $S$-act, $W$-injectivity, $PW$-injectivity, $C$-injectivity, strong regularity

Abstract

In the theory of S-acts, there exists a plethora of compelling
findings that establish connections between regularity in a monoid S
and injectivity (as well as other notions derived from injectivity) of Sacts. In this paper, we introduce the notion of strongly regular elements
in a hypermonoid as a generalization of regular elements in a monoid
and extends several classic results to hypermonoids and GHS-acts over
hypermonoids. Particularly, we show that S is strongly regular and
injective GHS-act if and only if all right ideals of S are C-injective.

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Published

2024-05-25

Issue

Vol. 18

Section

Vol. 18, No. 1, (2024)

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