Kehayopulu, Niovi; Tsingelis, Michael The ideal extensions of ordered semigroups. (English) Zbl 0902.06025 Bull. Greek Math. Soc. 38, 89-93 (1996). The theory of ideal extensions of semigroups developed by A. H. Clifford [Trans. Am. Math. Soc. 68, 165-175 (1950; Zbl 0037.01001)] is adopted here to partially ordered (p.o.) semigroups. A p.o. semigroup \(V\) is called an ideal extension of the p.o. semigroup \(S\) by the p.o. semigroup \(Q\) with zero as the least element if there exists a (semigroup and order) ideal \(T\) of \(V\) such that 1) \(T\) is isomorphic to \(S\), and 2) the Rees quotient semigroup \(V/T\) endowed with the partial order inherited from \(V\) and the zero as the least element is isomorphic to \(Q\). The partial homomorphisms used by Clifford are supposed to be order-preserving, and a list of 13 conditions is given which allow the construction of all ideal extensions \(V\) of a given p.o. semigroup \(S\) by a p.o. semigroup \(Q\) with zero. No proofs are given. Reviewer: H.Mitsch (Wien) MSC: 06F05 Ordered semigroups and monoids Keywords:partially ordered semigroup; ideal extensions; Rees quotient semigroup; partial homomorphisms Citations:Zbl 0037.01001 PDFBibTeX XMLCite \textit{N. Kehayopulu} and \textit{M. Tsingelis}, Bull. Greek Math. Soc. 38, 89--93 (1996; Zbl 0902.06025) Full Text: EuDML