On the Semigroup of Partial Isometries of a Finite Chain

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

doi:10.1080/00927872.2014.984838

On the Semigroup of Partial Isometries of a Finite Chain

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

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	639-647
Number of pages	9
Journal	Communications in Algebra
Volume	44
Issue number	2
DOIs	https://doi.org/10.1080/00927872.2014.984838
Publication status	Published - Feb 1 2016

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2014.984838

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title = "On the Semigroup of Partial Isometries of a Finite Chain",

abstract = "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.",

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author = "F. Al-Kharousi and R. Kehinde and A. Umar",

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AU - Al-Kharousi, F.

AU - Kehinde, R.

AU - Umar, A.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

KW - Height and fix of a transformation

KW - Partial isometries

KW - Partial one-to-one transformation

KW - Reflections and idempotents

KW - Translations

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JO - Communications in Algebra

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On the Semigroup of Partial Isometries of a Finite Chain

Abstract

Keywords

ASJC Scopus subject areas

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