SUBSEMIGROUPS GENERATED BY QUASI-IDEMPOTENTS IN CERTAIN FINITE SEMIGROUPS OF MAPPINGS
SUBSEMIGROUPS GENERATED BY QUASI-IDEMPOTENTS IN CERTAIN FINITE SEMIGROUPS OF MAPPINGS
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Date
2013-05
Authors
TANKO, IMAM,
Abdussamad
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Abstract
Abstract
Let Xn be the nite set f1; 2; : : : ; ng and let Tn and In be the full transformation
semigroup and the symmetric inverse semigroup on Xn respectively. In this the-
sis, we consider quasi-idempotent elements in the two semigroups Tn and In. For
the semigroup Tn, we characterise quasi-idempotent elements and establish that
the subsemigroup Singn of all singular self-maps of Tn is generated by a set of
quasi-idempotents called quasi-idempotents of type one. We also obtained the quasi-
idempotent rank of Singn. This number coincides with the rank and idempotent
rank of Singn which is 1
2n(n 1). For the semigroup In, we characterise quasi-
idempotent elements and prove that the subsemigroup SIn, of all strictly partial
injections of In, is generated by quasi-idempotents of type one.
Description
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA,
NIGERIA
Keywords
SUBSEMIGROUPS,, GENERATED,, QUASI-IDEMPOTENTS,, CERTAIN,, FINITE,, SEMIGROUPS,, MAPPINGS