Kehayopulu, Niovi; Tsingelis, Michael The embedding of an ordered semigroup into an le-semigroup. (English) Zbl 1044.06007 Lobachevskii J. Math. 13, 45-50 (2003). Let \(S\) be an ordered semigroup, \(\mathcal {P}(S)\) be the set of all subsets of \(S\). The authors prove that the set \(\mathcal{P}(S)\) with the multiplication \(\circ\) on \(\mathcal{P}(S)\) defined by \(A\circ B: = (AB]\) if \(A,B\in \mathcal{P}(S)\), \(A\not=\emptyset, B\not= \emptyset,\) and \(A\circ B: = \emptyset\) if \(A =\emptyset,\) or \(B = \emptyset\), is an le-semigroup having a zero element. Furthermore, \(S\) is embedded in \(\mathcal {P} (S)\). Reviewer: Xie Xiang-Yun (Guangdong) MSC: 06F05 Ordered semigroups and monoids Keywords:ordered semigroup; le-semigroup PDFBibTeX XMLCite \textit{N. Kehayopulu} and \textit{M. Tsingelis}, Lobachevskii J. Math. 13, 45--50 (2003; Zbl 1044.06007) Full Text: EuDML EMIS