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Matematicheskie Zametki, 2022, Volume 111, Issue 4, Pages 494–505
DOI: https://doi.org/10.4213/mzm13343 (Mi mzm13343) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Completely Prime Ideals in Multiplicatively Idempotent Semirings

E. M. Vechtomov, A. A. Petrov

Vyatka State University
Full-text PDF (450 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm13343
Abstract: Structure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in multiplicatively idempotent semirings are obtained. The main theorem describes the commutative multiplicatively idempotent semirings with zero in which all completely prime ideals are maximal: up to isomorphism, such semirings are exhausted by direct products of a Boolean ring and a generalized Boolean lattice. Examples are given showing that the conditions of commutativity and the presence of zero are essential.
Keywords: semiring, multiplicatively idempotent semiring, completely prime ideal, maximal ideal, commutativity, Boolean ring, generalized Boolean lattice.
Received: 01.11.2021
Revised: 11.11.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 4, Pages 515–524
DOI: https://doi.org/10.1134/S0001434622030191
Bibliographic databases:
Document Type: Article
UDC: 512.558
Language: Russian
Citation: E. M. Vechtomov, A. A. Petrov, “Completely Prime Ideals in Multiplicatively Idempotent Semirings”, Mat. Zametki, 111:4 (2022), 494–505; Math. Notes, 111:4 (2022), 515–524
Citation in format AMSBIB
\Bibitem{VecPet22}
\by E.~M.~Vechtomov, A.~A.~Petrov
\paper Completely Prime Ideals in Multiplicatively Idempotent Semirings
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 4
\pages 494--505
\mathnet{http://mi.mathnet.ru/mzm13343}
\crossref{https://doi.org/10.4213/mzm13343}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=594365}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 4
\pages 515--524
\crossref{https://doi.org/10.1134/S0001434622030191}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128824362}
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  • https://www.mathnet.ru/eng/mzm/v111/i4/p494
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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