Abstract
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.
Original language | English |
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Pages (from-to) | 327-336 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 79 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2009 |