Representation theory of finite semigroups over semirings

Zur Izhakian, John Rhodes, Benjamin Steinberg

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the results for a field. Special attention is paid to the boolean semiring, where we also characterize the simple representations and introduce the beginnings of a character theory.
Original languageEnglish
Pages (from-to)139-157
Number of pages19
JournalJournal of Algebra
Issue number1
Early online date20 Apr 2011
Publication statusPublished - 15 Jun 2011


  • representations
  • semirings
  • semigroups


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