Sen, M. K.; Saha, N. K. On \(\Gamma\)-semigroup. I. (English) Zbl 0601.20063 Bull. Calcutta Math. Soc. 78, 180-186 (1986). M is called a \(\Gamma\)-semigroup if axb\(\in M\) and \((axb)yc=ax(byc)\) for all a,b,c\(\in M\) and all x,y\(\in \Gamma\), where M and \(\Gamma\) are two non-empty sets. Let \(x\in \Gamma\) be a fixed element, then \(M_ x=(M,\circ)\), where \(a\circ b=axb\) for all a,b\(\in M\), is a semigroup. A \(\Gamma\)-semigroup M is called a \(\Gamma\)-group if \(M_ x\) is a group. There are defined \(\Gamma\)-subsemigroups, regular \(\Gamma\)-semigroups, simple left (right) \(\Gamma\)-semigroups,... The authors present several examples and a construction of \(\Gamma\)-semigroups and conditions when a regular \(\Gamma\)-semigroup is a \(\Gamma\)-group. Reviewer: E.Brozikova Cited in 8 ReviewsCited in 51 Documents MSC: 20M99 Semigroups 20N99 Other generalizations of groups 20M10 General structure theory for semigroups 20M50 Connections of semigroups with homological algebra and category theory Keywords:\(\Gamma \)-subsemigroups; regular \(\Gamma \)-semigroups; \(\Gamma \)-group PDFBibTeX XMLCite \textit{M. K. Sen} and \textit{N. K. Saha}, Bull. Calcutta Math. Soc. 78, 180--186 (1986; Zbl 0601.20063)