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INJECTIVE TRANSFORMATIONS WITH EQUAL GAP AND DEFECT
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 79 / Issue 2 / April 2009
- Published online by Cambridge University Press:
- 13 March 2009, pp. 327-336
- Print publication:
- April 2009
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- Article
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Suppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α∈I(X), we let dom α and ran α denote the domain and range of α, respectively, and we say that g(α)=|X/dom α| and d(α)=|X/ran α| is the ‘gap’ and the ‘defect’ of α, respectively. In this paper, we study algebraic properties of the semigroup
. For example, we describe Green’s relations and ideals in A(X), and determine all maximal subsemigroups of A(X) when X is uncountable.
. For example, we describe Green’s relations and ideals in 