On finite congruence-simple semirings

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In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zero-multiplication rings of prime order, matrix rings over finite fields, ones with trivial addition, and those that are additively idempotent.

Original languageEnglish
Pages (from-to)846-854
Number of pages9
JournalJournal of Algebra
Issue number2
StatePublished - Jan 15 2004


  • Congruence free
  • Congruence simple
  • Semirings

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