Rendiconti del Circolo Matematico di Palermo

, Volume 28, Issue 1, pp 80–90 | Cite as

Anneaux polynomiaux a deux variables

  • Alfred Doneddu


Some types of extensions of skew fields are now known: Galois quadratic extensions ([7]), cyclic extensions ([1]), general quadratic extensions ([4]), binomial extensions ([5]). All these extensions belong to the class of pseudolinear extensions ([8]).

A new class of extensions, the so-called «hexaphic extensions», which extends the class of pseudo-linear extensions, will be studied in the other papers in future. For this study, we introduce in this paper skew polynomials rings in two variables over a ring, which extend the well-known skew polynomial rings in one variable (pseudolinear) first studied by O. Ore ([10]).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Amitsur A. S.,Non-commutative cyclic extensions, Duke Math. J.,21 (1954), 87–105.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Cohn P. M.,On the free product of associative rings, Math. Z.,71 (1959), 380–398.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Cohn P. M.,On the free product of associative rings II, the case of skew fields, Math. Z.,73 (1960), 433–456.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Cohn P. M.,Quadratic extensions, of skew fields, Proc. L.M.S.11 (1961), 531–556.MATHCrossRefGoogle Scholar
  5. [5]
    Cohn P. M.,On a class of binomial extensions, Illinois J. Math.,10 (1966), 418–424.MATHMathSciNetGoogle Scholar
  6. [6]
    Cohn P. M.,Free rings and their relations, Acadamic Press, London (1971)MATHGoogle Scholar
  7. [7]
    Dieudonné J.,Les extensions quadratiques des corps non commutatifs et leurs applications, Acta Math.,87 (1952), 175–242.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Doneddu A.,Extensions pseudo-linéaires finies des corps non commutatifs, Journal of Algebra,28 (1974) 57–87.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Jacobson N.,Structure of rings, Amer. Math. Soc. Providence (1968).Google Scholar
  10. [10]
    Ore O.,Theory of non-commutative polynomials, Ann. of Math., (2)34 (1933), 81–94.MathSciNetGoogle Scholar

Copyright information

© Springer 1979

Authors and Affiliations

  • Alfred Doneddu
    • 1
  1. 1.VersaillesFrancia

Personalised recommendations