Algebra and Discrete Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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}
Linking options:
  • https://www.mathnet.ru/eng/adm367
  • https://www.mathnet.ru/eng/adm/y2003/i1/p32
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:128
    Full-text PDF :64
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024