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
SN - 0308-2105
VL - 123
SP - 355
EP - 363
JO - Royal Society of Edinburgh - Proceedings A
JF - Royal Society of Edinburgh - Proceedings A
IS - 2
ER -