Non-characteristic approximate roots of polynomials
Let \(K\) be a field and \(K((X))\) the Laurent series in the variable \(X\) with coefficients in \(K\). Let \(f(Y)\in K((X))[Y]\) be a monic and irreducible polynomial. For any positive integer \(l\) dividing \(\deg_Yf\) the approximate \(l-th\) root of \(f\) is a monic polynomial \(g(Y)\in K((X))[Y]\) such that \(\deg_Y(f-g^l) < \deg_Yf -{\deg_Yf\over l}\). The approximate \(l\)-th root exists and is uniquely determined. In this paper, the author extends Abhyankar-Moh results about this notion known in the case of characteristic degree to the case of non characteristic degree.
scientific article; zbMATH DE number 6005461