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Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 376-383 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

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