Regular elements and Green's relations in generalized transformation semigroups

S. Mendes-Gonçalves, Robert Sullivan, V. Gould

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    If X and Y are sets, we let P(X, Y) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). If θ ∈ P(Y, X), then P(X, Y) is a so-called "generalized semigroup" of transformations under the "sandwich operation": α * β = α θ β, for each α, β ∈ P(X, Y). We denote this semigroup by P(X, Y, θ) and, in this paper, we characterize Green's relations on it: that is, we study equivalence relations which determine when principal left (or right, or 2-sided) ideals in P(X, Y, θ) are equal. This solves a problem raised by Magill and Subbiah in 1975. We also discuss the same idea for important subsemigroups of P(X, Y, θ) and characterize when these semigroups satisfy certain regularity conditions. © 2013 World Scientific Publishing Company.
    Original languageEnglish
    Pages (from-to)1350006-1 - 1350006-11
    JournalAsian-European Journal of Mathematics
    Volume6
    Issue number1
    DOIs
    Publication statusPublished - 2013

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