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Semigroup Forum

, Volume 5, Issue 1, pp 262–269 | Cite as

Free inverse semigroups

  • W. D. Munn
Research Announcements

Abstract

Various methods have been given for establishing the existence of the free inverse semigroup FIA on a set A, and for constructing it explicitly (see, for example, [2], [5], [7], [9], [10], [11]). In this paper we outline a graph-theoretic technique for representing the elements of FIA. This depends on the notion, introduced here, of a word-tree on A. With the aid of this technique various properties of FIA are easily deduced: some of these are stated below.

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References

  1. 1.
    Clifford, A.H. and G.B. Preston,The algebraic theory of semigroups, Vol. I, Amer. Math. Soc. Surveys No. 7 (Providence, R.I., 1961).Google Scholar
  2. 2.
    Eberhart, C. and J. Selden,One parameter inverse semigroups (to appear).Google Scholar
  3. 3.
    Evans, T.,Finitely presented loops, lattices, etc.are hopfian, J. London Math. Soc. 44 (1969), 551–552.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gluskin, L.M.,Elementary generalised groups, Mat. Sbornik 41 (83) (1957), 23–36. [Russian]MathSciNetGoogle Scholar
  5. 5.
    McAlister, D.B.,A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    O'Carroll, L., Private communication (April, 1972).Google Scholar
  7. 7.
    Preston, G.B.,Free inverse semigroups (to appear).Google Scholar
  8. 8.
    Reilly, N.R.,Free generators in free inverse semigroups (to appear).Google Scholar
  9. 9.
    Scheiblich, H.E.,Free inverse semigroups (to appear).Google Scholar
  10. 10.
    Schein, B.M., Research problem #21, Semigroup Forum 3 (1971), 281.Google Scholar
  11. 11.
    Vagner, V.V.,Generalised heaps and generalised groups with a transitive compatibility relation, Učenye Zapiski Saratov. Gos. Univ., meh.-matem., 70 (1961), 25–39. [Russian]Google Scholar

Copyright information

© Springer-Verlag New York Inc 1973

Authors and Affiliations

  • W. D. Munn
    • 1
  1. 1.Department of MathematicsThe UniversityStirlingScotland

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