Semigroup Forum

, 42:265 | Cite as

Oids, finite sums and the structure of the Stone-Čech compactification of a discrete semigroup

  • Talin Papazyan
Research Article


The equivalence between oids and semigroups which satisfy a condition involving finite sums is established. Some of the already known results on the structure of Stone-Čech compactifications of discrete semigroups are obtained as immediate consequences. It is also shown that most commutative semigroups contain oids so that oid theory has applications to the Stone-Čech compactifications of many semigroups.


Finite Subset Commutative Semigroup Minimal Ideal Minimal Left Ideal Disjoint Copy 


  1. [1]
    Clifford, a. H. and G. B. Preston, “The algebraic theory of semigroups,” Volume I. American Mathematical Society, 1961.Google Scholar
  2. [2]
    Comfort, W. and S. Negrepontis, “The theory of ultrafilters,” Springer-Verlag, Berlin, 1974.MATHGoogle Scholar
  3. [3]
    van Douwen, E.,The Čech-Stone compactification of a discrete groupoid. Topology Appl. (to appear).Google Scholar
  4. [4]
    Ellis, R., “Lectures on topological dynamics,” Benjamin, New York, 1969.MATHGoogle Scholar
  5. [5]
    Hindman, N.,The ideal structure of the space of κ-uniform ultrafilters on a discrete semigroup, Rocky Mountain J. Math.16 (1986), 685–701.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Hindman, N. and J.S. Pym,Free groups and scmigroups in βN, Semigroup Forum30 (1984), 177–193.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Lisan, A. T.,Free groups in βNwhich miss the minimal ideal, Semigroup Forum37 (1988), 233–239.MATHMathSciNetGoogle Scholar
  8. [8]
    Pym, J. S.,Semigroup structure in Stone-Čech compactifications, J. London Math. Soc.36 (1987), 421–428.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Walker, R. C., “The Stone-Čech compactification,” Springer-Verlag, 1974.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Talin Papazyan
    • 1
    • 2
  1. 1.Department of Pure MathematicsThe UniversitySheffieldEngland
  2. 2.Matematik BolumuBogazici UniversitesiBebek IstanbulTurkey

Personalised recommendations