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The ideal extensions of ordered semigroups. (English) Zbl 0902.06025

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

Citations:

Zbl 0037.01001
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