Ivan Chajda, Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: ivan.chajda@upol.cz; Helmut Länger, Institute of Discrete Mathematics and Geometry, Faculty of Mathematics and Geoinformation, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria, e-mail: helmut.laenger@tuwien.ac.at; Filip Švrček, Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: filip.svrcek@upol.cz
Abstract: 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.
Keywords: semiring; commutative semiring; multiplicatively idempotent semiring; semiring of characteristic 2; simple semiring; unitary Boolean ring; bounded distributive lattice
Classification (MSC 2010): 16Y60, 06E20
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