Anneaux polynomiaux a deux variables

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]).