Advertisement

The Influence of Menger’s Ideas on the Work of Nöbauer and His School

  • H. Kaiser
Chapter
  • 68 Downloads

Abstract

Shortly after the Second World War Wilfried Nöbauer was studying mathematics at the University od Vienna. He asked Edmund Hlawka, the eminent number theorist at the university, to be the supervisor of his doctoral dissertation. Hlawka proposed taking a paper of Eckmann on the uniform distribution of values of the exponential function as a starting point for the research. Nöbauer did, but deviated from the originally intended analytic line of research and pursued instead an algebraic idea in Eckmann’s paper. This resulted in a systematic study of permutation polynomials (see below).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Dorfer, H. Woracek: Formal Power Series and Some Theorems of J. F. Ritt in Arbitrary Characteristic. Monatsh. f. Math. 127 (1999) 277–293.MathSciNetCrossRefGoogle Scholar
  2. G. Eigenthaler, H. Woracek: Permutable Polynomials and Related Topics. Contributions to General Algebra 9 (1995) 163–182.MathSciNetzbMATHGoogle Scholar
  3. M. Istinger, H. Kaiser, A. Pixley: Interpolation in Congruence Permutable Algebras. Colloquium Math. 42 (1979) 219–239.MathSciNetzbMATHGoogle Scholar
  4. H. Kaiser, W. Nöbauer: Uber interpolierbare Funktionen auf universalen Algebren. Beiträge zur Algebra und Geometrie 12 (1982) 51–55.zbMATHGoogle Scholar
  5. E. Fried, H. Kaiser, L. Marki: An Elementary Approach to Polynomial Interpolation in Universal Algebras. Alg. Univ. 15 (1982) 40–57.MathSciNetCrossRefGoogle Scholar
  6. H. Kaiser: Interpolation in Universal Algebras. In: P. Burmeister et al. (eds.), Universal Algebra and its Links with Logic, 29–40. Berlin: Heldermann, 1984.Google Scholar
  7. H. Kaiser, W. Nöbauer: Permutation Polynomials in Several Variables Over Residue Class Rings. J. Austral. Math. Soc. 43 (1987) 171–175.MathSciNetCrossRefGoogle Scholar
  8. H. Länger: Zur Theorie der superassoziativen Systeme und Menger-Algebren. Ph. D. Diss, Vienna University of Technology, 1976Google Scholar
  9. H. Länger: Commutative Quasi-trivial Superassociative Systems. Fund. Math. 109 (1980) 79–88.MathSciNetCrossRefGoogle Scholar
  10. H. Lausch, W. Nöbauer: Algebra of Polynomials. North-Holland, Amsterdam-London, 1973. R. Lidl, W. B. Müller: On Commutative Semigroups of Polynomials with Respect to Composition. Monatsh. f. Math. 102 (1986) 139–153.CrossRefGoogle Scholar
  11. R. Lidl, W. B. Müller: Permutation Polynomials in RSA-Cryptosystems. In: D. Charm (ed.), Advances in Cryptology, 293–301. New York: Plenum, 1984.CrossRefGoogle Scholar
  12. H. Mitsch: Trioperationale Algebren über Verbänden. Ph. D. Diss. Univ. Wien, 1967. W. B. Müller: Derivationen in Kompositionsalgebren Sitzungsber. der Oster. Akad. d. Wiss. Math-nat. Kl. 184 (1975) 239–243.Google Scholar
  13. W. B. Müller: Eindeutige Abbildungen mit Summen-, Produkt-und Kettenregel im Polynomring Monatsh. f. Math. 73 (1969) 354–367.CrossRefGoogle Scholar
  14. G. Pilz: Near Rings. North-Holland, Amsterdam-New York-Oxford, 1977.Google Scholar
  15. R. Pöschel, L. A. Kaluznin: Funktionen-und Relationenalgebren. Birkhäuser, Basel-Stuttgart 1979.CrossRefGoogle Scholar
  16. I. G. Rosenberg: Ober die funktionale Vollständigkeit in den mehrwertigen Logiken, Rozpr. CSAV Rada Mat. Prir. Ved., Praha 80, 4 (1970) 3–93.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • H. Kaiser

There are no affiliations available

Personalised recommendations