Baer-Levi Semigroups of Partial Transformations

F.A. Pinto, Robert Sullivan

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    Let X be an infinite set and suppose א0 ≤ q ≤ |X|. The Baer-Levi semigroup on X is the set of all injective ‘total’ transformations α: X → X such that |X\Xα| = q. It is known to be a right simple, right cancellative semigroup without idempotents, its automorphisms are “inner”, and some of its congruences are restrictions of Malcev congruences on I(X), the symmetric inverse semigroup on X. Here we consider algebraic properties of the semigroup consisting of all injective ‘partial’ transformations α of X such that |X\Xα| = q: in particular, we descried the ideals and Green's relations of it and some of its subsemigroups.
    Original languageEnglish
    Pages (from-to)87-106
    JournalBulletin of the Australian Mathematical Society
    Volume69
    Issue number1
    DOIs
    Publication statusPublished - 2004

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