Generating sets of completely 0-simple semigroups

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Abstract

A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M-0[G ; I , Lambda; P], is given. The result generalizes that of Ruskuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of vertical bar I vertical bar, vertical bar Lambda vertical bar, the number of connected components k of P, and a number r(min), which we define. We go on to show that the number r(min) is expressible in terms of a family of subgroups of G , the members of which are in one-to-one correspondence with, and determined by the nonzero entries of, the components of P . A number of applications are given, including a generalization of a result of Gomes and Howie concerning the rank of an arbitrary Brandt semigroup B ( G ,{1,..., n }).

Original languageEnglish
Pages (from-to)4657-4678
JournalCommunications in Algebra
Volume33
Issue number12
DOIs
Publication statusPublished - 2005

Keywords

  • 0-simple semigroups
  • minimal generating sets
  • rank
  • RANK

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