TY - JOUR

T1 - On the semigroups of partial one-to-one order-decreasing finite transformations

AU - Umar, Abdullahi

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

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U2 - 10.1017/S0308210500025737

DO - 10.1017/S0308210500025737

M3 - Article

AN - SCOPUS:84972102836

VL - 123

SP - 355

EP - 363

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -