A note on maximal ideals in ordered semigroups

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2003
• Hauptverfasser: Kehayopulu, N., Ponizovskii, J., Tsingelis, M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/154673
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: A note on maximal ideals in ordered semigroups / N. Kehayopulu, J. Ponizovskii, M. Tsingelis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 32–35. — Бібліогр.: 3 назв. — англ.

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 order...