Some Results on Γ-Acts over Γ-Semigroups

Some Results on Γ-Acts over Γ-Semigroups

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 aΓ-act over a Γ-semigroup is a generalization of actions over semigroups. In this paper, certain intrinsic and basic properties of 􀀀-acts including cyclic, indecomposable and free are studied as well. Among other results, it is also shown that aΓ-act is free only ifΓ = 1.