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

Abdullahi Umar

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] 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 In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in Jn-1.

Original languageEnglish
Pages (from-to)355-363
Number of pages9
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume123
Issue number2
DOIs
Publication statusPublished - 1993

ASJC Scopus subject areas

  • Mathematics(all)

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