Archimedean ordered semigroups as ideal extensions |
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| Authors: | Niovi Kehayopulu Michael Tsingelis |
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| Institution: | (1) Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece;(2) Department of Electrological Engineering, Technological Educational Institute of Patras, Megalou Alexandrou 1, 26334 Koukouli, Patras, Greece |
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| Abstract: | The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We
prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup
containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an
ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. |
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| Keywords: | Ideal extension of an ordered semigroup by an ordered semigroup Archimedean ordered semigroup Idempotent element Ideal Simple ordered semigroup Nil ordered semigroup The Rees quotient ordered semigroup |
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