Geodesic
Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 376-383.

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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. 
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E. M. Vechtomov; A. A. Petrov. Multiplicatively Idempotent Semirings in which All Congruences Are Ideal. Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 376-383. http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a5/

[1] E. M. Vechtomov, A. A. Petrov, “Prostye idealy v multiplikativno idempotentnykh polukoltsakh”, Matem. zametki, 111:4 (2022), 494–505 | DOI

[2] J. S. Golan, Semirings and Their Applications, Kluwer Acad. Publ., Dordrecht, 1999 | MR

[3] V. P. Maslov, V. N. Kolokoltsov, Idempotentnyi analiz i ego primenenie v optimalnom upravlenii, Nauka, M., 1994 | MR

[4] G. Grettser, Obschaya teoriya reshetok, Mir, M., 1982 | MR

[5] L. A. Skornyakov, Elementy teorii struktur, Nauka, M., 1982 | MR

[6] I. Lambek, Koltsa i moduli, Mir, M., 1971 | MR

[7] R. Sikorskii, Bulevy algebry, Mir, M., 1969 | MR

[8] E. M. Vechtomov, “Annulyatornye kharakterizatsii bulevykh kolets i bulevykh reshetok”, Matem. zametki, 53:2 (1993), 15–24 | MR | Zbl