On Gamma Acts over Gamma Semigroups

Authors

  • Hamid Rasouli Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
  • Ali Reza Shabani Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Keywords:

Γ-semigroup, Γ-act, Γ-congruence

Abstract

For a semigroup S, actions of S on non-empty sets, namely S-acts, are of interest to consider for their applications in many branches of science. The well known generalization of a semigroup is the Γ-semigroup. The notion of a Γ-act over a Γ-semigroup is a generalization of actions over semigroups. In this paper, certain
intrinsic and basic properties of Γ-acts including cyclic, indecomposable and free are studied as well. Among other results, it is also shown that a Γ-act is free only if |Γ| = 1.

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Published

2017-07-11

Issue

Vol. 10 No. 4: (July 2017)

Section

Discrete Mathematics

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How to Cite

On Gamma Acts over Gamma Semigroups. (2017). European Journal of Pure and Applied Mathematics, 10(4), 739-748. https://www.ejpam.com/index.php/ejpam/article/view/2696