On the monoid of partial isometries with fixed set

Authors

  • M.M. Zubairu †Department of Mathematical Sciences, Bayero University, Kano, Nigeria
  • Z.D. Lawan Department of Science, School of Continuing Education, Bayero University, Kano, P.M.B 3011, Nigeria

Keywords:

partial isometries, fixed sets, semilattice, rank

Abstract

Denote [n] to be a finite n-chain 12n ,and let DPn denote the semigroup of all partial isometries on [n]. For a nonempty subset D of [n], let Fix([n]D) be the set of all maps in DPn which fix all elements of D. Then Fix([n]D) is a subsemigroup of DPn. In this paper, we show that the semigroup Fix([n]D) is a semilattice of idempotents, and further, we obtain the cardinality and the rank of the semigroup.

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Published

2025-03-01

How to Cite

Zubairu, M. ., & Lawan, Z. . (2025). On the monoid of partial isometries with fixed set. International Journal of Mathematical Analysis and Modelling, 7(2). Retrieved from https://tnsmb.org/journal/index.php/ijmam/article/view/188

Issue

Vol. 7 No. 2 (2024): Volume 7, Issue 2, 2024

Section

Articles