The Ranks of Ideals in Various Transformation Monoids

Abstract

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 Howie , J. M. , McFadden , R. B. ( 1990 ). Idempotent rank in finite full transformation semigroups . Proc. Royal Soc. Edinburgh A 114 : 161 – 167 .[Crossref], [Web of Science ®] , [Google Scholar]], we complete the study of the ranks (and of idempotent ranks, when applicable) of all their ideals.