A note on maximal ideals in ordered semigroups
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...
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| Datum: | 2003 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2003
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154673 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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. |
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