Abstract
30Jun 2016 GAMMA ACTS M.S. Abbas and Abdulqader faris Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Highlights
We introduce the notion of gamma act over Г-semigroup S and study some important properties of such acts, with this respect, we study gamma subacts, congruences and homomorphisms, of gamma acts further,we give related basic results of gamma acts .And we will show the class of gamma acts is a generalization of S-acts and Г-semigroups
The concept of S-act has been introduced as follows: if S is a semigroup, a nonempty set M is called a left S-act if there is a mapping from S×M into M and the following condition is satisfied : s1(s2m) = (s1s2)m for all s1,s2 ∈ S and m ∈ M [1]
Sen in 1981 as follows: if S and Г are nonempty sets, S is called a Г-semigroup if there is a mapping from S×Г×S into S and the following condition is satisfied :(s1αs2)βs3 = s1α (s2βs3) for all s1,s2,s3 ∈ S and α, β ∈ Г [2]
Summary
The concept of S-act has been introduced as follows: if S is a semigroup, a nonempty set M is called a left S-act if there is a mapping from S×M into M and the following condition is satisfied : s1(s2m) = (s1s2)m for all s1,s2 ∈ S and m ∈ M [1]. The concept of Г-semigroup has been introduced by M.K. Sen in 1981 as follows: if S and Г are nonempty sets, S is called a Г-semigroup if there is a mapping from S×Г×S into S and the following condition is satisfied :(s1αs2)βs3 = s1α (s2βs3) for all s1,s2,s3 ∈ S and α, β ∈ Г [2]. A nonempty subset A of a Г-semigroup S is called right ideal of S if AΓS ⊆ A where AΓS = { aαs | a ∈ A , α ∈ Г and s ∈ S }.
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