The Ranks of Ideals in Various Transformation Monoids

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In this paper we consider various classes of monoids of transformations of a finite chain, including those of transformations that preserve or reverse either the order or the orientation. In line with Howie and McFadden [24], we complete the study of the ranks (and of idempotent ranks, when applicable) of all their ideals.

Original languageEnglish
Pages (from-to)674-692
Number of pages19
JournalCommunications in Algebra
Issue number2
Publication statusPublished - 1 Feb 2015


  • Idempotent rank
  • Order-preserving
  • Orientation-preserving
  • Rank
  • Transformation


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