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.
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References
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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 376–383 https://doi.org/10.4213/mzm13521.
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Vechtomov, E.M., Petrov, A.A. Multiplicatively Idempotent Semirings in which All Congruences Are Ideal. Math Notes 112, 382–387 (2022). https://doi.org/10.1134/S0001434622090061
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DOI: https://doi.org/10.1134/S0001434622090061