2011/12/31 by Andreas Kendziorra, Kendziorra, Andreas, Jens Zumbrägel +1
Computer Science · Decision Sciences · #06A12 #16Y60 #Educational Technology and Assessment #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1201.0272
openalex publication_date 2011/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Since for the classification of finite (congruence-)simple semirings it remains to classify the 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.