On the semigroup of order-decreasing partial isometries of a finite chain · arXivDesk1101.2558Jan 13, 201111 pages
On the semigroup of order-decreasing partial isometries of a finite chain
R. Kehinde, S. O. Makanjuola, A. Umar
Abstract
Let In be the symmetric inverse semigroup on Xn={1,2,...,n}
and let
and
be its subsemigroups of order-decreasing partial isometries and of order-preserving order-decreasing partial isometries of
, respectively. In this paper we investigate the cycle structure of order-decreasing partial isometry and characterize the Green's relations on
and
. We show that
is a
0−E−unitary ample semigroup. We also investigate the cardinalities of some equivalences on
and
which lead naturally to obtaining the order of the semigroups.