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Matematicheskie Zametki, 2022, Volume 112, Issue 3, Pages 376–383
DOI: https://doi.org/10.4213/mzm13521 (Mi mzm13521) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Multiplicatively Idempotent Semirings in which All Congruences Are Ideal

E. M. Vechtomov, A. A. Petrov

Vyatka State University
Full-text PDF (404 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm13521
Abstract: The study of multiplicatively idempotent semirings with additional conditions is continued. It is proved that every multiplicatively idempotent semiring with ideal congruences is isomorphic to the direct product of a Boolean ring and a generalized Boolean lattice. Thus, a new abstract characterization is obtained for the direct products of Boolean rings and generalized Boolean lattices. Examples are given.
Keywords: semiring, multiplicatively idempotent semiring, ideal congruence, Boolean ring, generalized Boolean lattice.
Received: 01.04.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 3, Pages 382–387
DOI: https://doi.org/10.1134/S0001434622090061
Bibliographic databases:
Document Type: Article
UDC: 512.558
Language: Russian
Citation: E. M. Vechtomov, A. A. Petrov, “Multiplicatively Idempotent Semirings in which All Congruences Are Ideal”, Mat. Zametki, 112:3 (2022), 376–383; Math. Notes, 112:3 (2022), 382–387
Citation in format AMSBIB
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\by E.~M.~Vechtomov, A.~A.~Petrov
\paper Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 3
\pages 376--383
\mathnet{http://mi.mathnet.ru/mzm13521}
\crossref{https://doi.org/10.4213/mzm13521}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538774}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 3
\pages 382--387
\crossref{https://doi.org/10.1134/S0001434622090061}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140124426}
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    • This publication is cited in the following 1 articles:
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