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Algebra and Discrete Mathematics, 2003, Issue 1, Pages 32–35 (Mi adm367)  
This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

A note on maximal ideals in ordered semigroups

N. Kehayopulua, J. Ponizovskiib, M. Tsingelisa

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
Full-text PDF (124 kB) Citations (1)
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.
Received: 06.12.2002
Bibliographic databases:
Document Type: Article
MSC: 06F05
Language: English
Citation: N. Kehayopulu, J. Ponizovskii, M. Tsingelis, “A note on maximal ideals in ordered semigroups”, Algebra Discrete Math., 2003, no. 1, 32–35
Citation in format AMSBIB
\Bibitem{KehPonTsi03}
\by N.~Kehayopulu, J.~Ponizovskii, M.~Tsingelis
\paper A note on maximal ideals in ordered semigroups
\jour Algebra Discrete Math.
\yr 2003
\issue 1
\pages 32--35
\mathnet{http://mi.mathnet.ru/adm367}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2051637}
\zmath{https://zbmath.org/?q=an:1035.06003}
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    • This publication is cited in the following 1 articles:
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    		Algebra and Discrete Mathematics
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