Finite simple additively idempotent semirings

Mathematics – Rings and Algebras

Scientific paper

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30 pages, 1 figure

Scientific paper

Since for the classification of finite (congruence-)simple semirings it remains to classify all additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of join-morphisms of a semilattice. We succeed in doing this for many cases, amongst others for every semiring of this kind with an additively neutral element. As a consequence we complete the classification of finite simple semirings with an additively neutral element. To complete the classification of all finite simple semirings it remains to classify some very specific semirings, which will be discussed here. Our results employ the theory of idempotent irreducible semimodules, which we develop further.

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