Afrika Matematika

, Volume 25, Issue 3, pp 841–856

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

Article

DOI: 10.1007/s13370-013-0158-2

Cite this article as:
Heidari, D. & Davvaz, B. Afr. Mat. (2014) 25: 841. doi:10.1007/s13370-013-0158-2

Abstract

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.

Keywords

Semigroup\(\Gamma \)-semigroup\(n\)-ary \(\Gamma \)-semigroup

Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsYazd UniversityYazdIran