On the Semigroup of Partial Isometries of a Finite Chain
F. Al-Kharousi, Rotimi Kehinde, Abdullahi Umar Β· Communications in Algebra Β· 2015
Let βn be the symmetric inverse semigroup on Xn = {1, 2,β¦, n}, and let ππ«n and πͺππ«n 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 ππ«n and πͺππ«n. We show that πͺππ«n is a 0-E-unitary inverse semigroup. We also investigate the ranks of ππ«n and πͺππ«n.