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On extensions of partial orders of partially ordered semigroups. (Chinese. English summary) Zbl 1199.06058

Summary: In this paper, firstly, the concepts of semi-pseudoorder and semi-pseudochain mod \(\sigma\) on a partially ordered semigroup \( (S,\cdot,\leq)\) is introduced. Secondly, a sufficient condition for extending a partial order of \(S\) to another partial order by semi-pseudochain is given, and we obtain some interesting results. In particular, two semilattice homomorphism theorems are obtained. Finally, we give sufficient and necessary conditions for extending a partial order of \(S\) to another partial order such that some finite subsets satisfying some conditions of \(S\) form a chain.

MSC:

06F05 Ordered semigroups and monoids
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