Kehayopulu, Niovi On completely regular ordered semigroups. (English) Zbl 0905.06011 Sci. Math. 1, No. 1, 27-32 (1998). Summary: We wrote this paper in an attempt to show the way we pass from the results on ordered semigroups based on ideals to the results on semigroups – without order – based on ideals, and conversely. We tried to use sets instead of elements in the proof of our results as an example to show that in the theory of semigroups – without order – based on ideals, elements do not play any role, but the sets do. Besides, the results on semigroups – without order – based on ideals can be also obtained either by an easy modification of the results on ordered semigroups (by setting \(A\) instead of \((A])\) or as an application of the results on ordered semigroups in the way indicated in this paper. Cited in 15 Documents MSC: 06F05 Ordered semigroups and monoids 20M17 Regular semigroups Keywords:completely regular ordered semigroups; bi-ideal; quasi-ideal; semiprime subset Citations:Zbl 0448.20058 PDFBibTeX XMLCite \textit{N. Kehayopulu}, Sci. Math. 1, No. 1, 27--32 (1998; Zbl 0905.06011)