, Volume 25, Issue 3, pp 841-856
Date: 16 Apr 2013

\(n\) -ary \(\Gamma \) -semigroups, operators and Green’s relations

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In this paper, we define the concept of \(n\) -ary \(\Gamma \) -semigroups as a generalization of \(n\) -ary semigroups and a generalization of \(\Gamma \) -semigroups. We prove some results and present many examples of \(n\) -ary \(\Gamma \) -semigroups. Also, we introduce the concept of Green’s equivalence relations on \(n\) -ary \(\Gamma \) -semigroups and prove some properties. Then, the notion of operator \(n\) -ary semigroup of an \(n\) -ary \(\Gamma \) -semigroup is defined. Finally, we define the notion of \(n\) -ary \(\Gamma \) -group.