Representation theory of finite semigroups, semigroup radicals and formal language theory

Jorge Almeida, Stuart Margolis, Benjamin Steinberg, Mikhail Volkov

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving: triangularizability of finite semigroups; which semigroups have (split) basic semigroup algebras, two-sided semidirect product decompositions of finite monoids; unambiguous products of rational languages; products of rational languages with counter; and Černý's conjecture for an important class of automata.

Original languageEnglish
Pages (from-to)1429-1461
Number of pages33
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - Mar 2009


  • Language theory
  • Radicals
  • Representation theory


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