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On completely regular ordered semigroups. (English) Zbl 0905.06011

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.

MSC:

06F05 Ordered semigroups and monoids
20M17 Regular semigroups

Citations:

Zbl 0448.20058
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