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INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
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 Title & Authors
INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
Singha, Boorapa; Sanwong, Jintana; Sullivan, Robert Patrick;
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 Abstract
In 2003, Marques-Smith and Sullivan described the join of the 'natural order' and the 'containment order' on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective such that , where . In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of and on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since does not equal on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting.
 Keywords
partial transformation semigroup;Baer-Levi semigroup;inverse semigroup;natural order;containment order;meet and join;
 Language
English
 Cited by
 References
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