|
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
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
Citation:
N. Kehayopulu, J. Ponizovskii, M. Tsingelis, “A note on maximal ideals in ordered semigroups”, Algebra Discrete Math., 2003, no. 1, 32–35
Linking options:
https://www.mathnet.ru/eng/adm367 https://www.mathnet.ru/eng/adm/y2003/i1/p32
|
Statistics & downloads: |
Abstract page: | 128 | Full-text PDF : | 64 | First page: | 1 |
|