N. Kehayopulu, J. Ponizovskii, M. Tsingelis, “A note on maximal ideals in ordered semigroups”, Algebra Discrete Math., 2003, Issue 1,Pages <nobr>32

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RESEARCH ARTICLE

A note on maximal ideals in ordered semigroups

N. Kehayopulu^a, J. Ponizovskii^b, M. Tsingelis^a

^a University of Athens, Department of Mathematics Section of algebra and geometry, Panepistemiopolis, Athens 157 84, Greece
^b Russian State Hydrometeorological University Department of Mathematics Malookhtinsky pr. 98 195196, Saint-Petersburg, Russia

Abstract: In commutative rings having an identity element, every maximal ideal is a prime ideal, but the converse statement does not hold, in general. According to the present note, similar results for ordered semigroups and semigroups-without order-also hold. In fact, we prove that in commutative ordered semigroups with identity each maximal ideal is a prime ideal, the converse statement does not hold, in general.

Keywords: maximal ideal, prime ideal in ordered semigroups.

MSC: 06F05

Received: 06.12.2002

Language: English