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On the semigroups of partial one-to-one order-decreasing finite transformations

Published online by Cambridge University Press:  14 November 2011

Abdullahi Umar
Abdullahi Umar
Affiliation:
Department of Mathematical Sciences, University of St Andrews, St Andrews, KY16 9SS, Scotland, U.K
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Synopsis

Let In be the symmetric inverse semigroup on Xn = {1,…, n}, let Sln be the subsemigroup of strictly partial one-to-one self-maps of Xn and let = { α ∊ SIn: x} ≦ x = U = ∅= be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that is an (irregular, for n ≧ 2) type A semigroup with n D*-classes and D* = I*. Further, it is shown that is generated by the n(n + l)/2 quasi-idempotents in

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 355 - 363
Copyright
Copyright © Royal Society of Edinburgh 1993

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