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Semigroup Forum

, Volume 39, Issue 1, pp 311–322 | Cite as

A functional treatment of right invariant right holoids

  • Ludwig Cottin
Research Article
  • 15 Downloads

Abstract

Through this paper we are concerned with right invariant right holoids which are semigroups with left cancellation rule, ordered by right divisibility. We are able to give a structure theorem under weak additional assumptions. In the proof we use factorsystems which occur in homological algebra.

Keywords

Exact Sequence Factor System Positive Cone Structure Theorem Shift Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    BESSENRODT, C., H. H. BRUNGS, G. TÖRNER, Chain Rings, Part IIa, Schriftenreihe der Universität Duisburg, Nr. 52 Preprint (1986).Google Scholar
  2. [2]
    BOTTO-MURA, R. T., H. H. BRUNGS, J. FISHER, Chain Rings and Valuation Semigroups, Comm. Algebra5 (1977) 14, 1529–1547.zbMATHMathSciNetGoogle Scholar
  3. [3]
    BROWN, K., Cohomology of Groups, Berlin, Heidelberg, New York, Springer 1982.zbMATHGoogle Scholar
  4. [4]
    BRUNGS, H. H., G. TÖRNER, Right Invariant Right Holoids, submitted for publication in Comm. Algebra.Google Scholar
  5. [5]
    CLIFFORD, A. H., Naturally Totally Ordered Commutative Semigroups, Amer. Jour. Math.76 (1954), 631–646.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    COTTIN, L., Rechtsinvariante Rechtsholoide endlichen Ranges, Dissertation, Duisburg, 1987.Google Scholar
  7. [7]
    FUCHS, L., Teilweise geordnete Strukturen, Göttingen, Vandenhoeck & Ruprecht 1966.zbMATHGoogle Scholar
  8. [8]
    KLEIN-BARMEN, F., Ein Beitrag zur Theorie der linearen Holoide, Math. Z.51 (1948), 355–366.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    SATYANARAYANA, M., Positively ordered Semigroups, New York, Marcel Dekker (1979).zbMATHGoogle Scholar
  10. [10]
    SCHEIN, B. M., On the Theory of Inverse Semigroups and Generalized Groups, Amer. Math. Soc. Trans. II113 (1979), 89–122.Google Scholar
  11. [11]
    SCHILLING, O. F. G., The Theory of Valuations, Math. Surveys, No. 4, Amer. Math. Soc., Providence, R.I. 1950.zbMATHGoogle Scholar
  12. [12]
    SKORNIAKOV, L. A., Left Valuation Semigroups, Sibirian Math. J.11 (1970), 135–145.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Ludwig Cottin
    • 1
  1. 1.Dept. of MathematicsUniversity of DuisburgDuisburg 1West Germany

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