Shao, Haiqin; Xue, Zhanjun; Lei, Zhenya On extensions of partial orders of partially ordered semigroups. (Chinese. English summary) Zbl 1199.06058 Pure Appl. Math. 24, No. 4, 730-735 (2008). 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 Keywords:partially ordered semigroup; partially ordered extension; semi-pseudoorder; semi-pseudochain; finitely totally ordered extension PDFBibTeX XMLCite \textit{H. Shao} et al., Pure Appl. Math. 24, No. 4, 730--735 (2008; Zbl 1199.06058)