Idempotent rank in the endomorphism monoid of a non-uniform partition

Igor Dolinka, James East, James D. Mitchell

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a non-uniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.
Original languageEnglish
Pages (from-to)73-91
JournalBulletin of the Australian Mathematical Society
Volume93
Issue number1
Early online date10 Aug 2015
DOIs
Publication statusPublished - Feb 2016

Keywords

  • Transformation semigroups
  • Idempotents
  • Generators
  • Rank
  • Idempotent rank

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