Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: R. Kehinde, S. O. Makanjuola and A. Umar
Pages: [51] - [65]
Received Date: December 1, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121903
Let 
be the symmetric inverse semigroup on
and let 
and 
be its subsemigroups of order-decreasing
partial isometries and of order-preserving and order-decreasing
partial isometries of 
respectively. In this paper, we investigate the
cycle structure of an order-decreasing partial isometry and
characterize the starred Green’s relations on and We show that is an ample semigroup and is a 0-E-unitary ample semigroup. We
also investigate the ranks of and 
partial one-to-one transformation, partial isometries, height, right (left) waist, right (left) shoulder and fix of a transformation, translations, reflections and idempotents rank of a semigroup.
