Algebraic Properties of the Semigroup of Partial Isometries of a Finite Chain

Abstract

This work analyses the algebraic properties of the sub-semi group of partial Isometries (〖DP〗_n) and of order preserving partial isometries (〖ODP〗_n) of a finite chain X_n={1,2,…n}, with a symmetric inverse semigroup I_n defined on it. It also investigates the subsemigroups 〖DP〗_n and 〖ODP〗_n for cycle structure and shows that 〖ODP〗_n is a 0 -E- unitary inverse semigroup.