Geodesic
Multiplicatively idempotent semirings
Mathematica Bohemica, Tome 140 (2015) no. 1, pp. 35-42

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Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices. We get a characterization of this join.
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices. We get a characterization of this join.
DOI : 10.21136/MB.2015.144177
Classification : 06E20, 16Y60
Keywords: semiring; commutative semiring; multiplicatively idempotent semiring; semiring of characteristic 2; simple semiring; unitary Boolean ring; bounded distributive lattice 
Chajda, Ivan; Länger, Helmut; Švrček, Filip. Multiplicatively idempotent semirings. Mathematica Bohemica, Tome 140 (2015) no. 1, pp. 35-42. doi: 10.21136/MB.2015.144177
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