On the Semigroup of Partial Isometries of a Finite Chain

F. Al-Kharousi, R. Kehinde, A. Umar

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13 Scopus citations


Let ℐn be the symmetric inverse semigroup on Xn = {1, 2,…, n}, and let 𝒟𝒫n and 𝒪𝒟𝒫n be its subsemigroups of partial isometries and of order-preserving partial isometries of Xn, respectively. In this article, we investigate the cycle structure of a partial isometry and characterize the Green's relations on 𝒟𝒫n and 𝒪𝒟𝒫n. We show that 𝒪𝒟𝒫n is a 0-E-unitary inverse semigroup. We also investigate the ranks of 𝒟𝒫n and 𝒪𝒟𝒫n.

Original languageBritish English
Pages (from-to)639-647
Number of pages9
JournalCommunications in Algebra
Issue number2
StatePublished - 1 Feb 2016


  • Height and fix of a transformation
  • Partial isometries
  • Partial one-to-one transformation
  • Reflections and idempotents
  • Translations


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