Injective Transformations with equal gap and defect

J. Sanwong, Robert Sullivan

    Research output: Contribution to journalArticle

    1 Citation (Scopus)


    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 languageEnglish
    Pages (from-to)327-336
    JournalBulletin of the Australian Mathematical Society
    Issue number2
    Publication statusPublished - 2009

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