Algebraic Division Ring Extensions1

On One-Sided Ideals of Rings of Linear Transformations

An Effective Weierstrass Division Theorem

We prove an effective Weierstrass Division Theorem for algebraic restricted power series with p-adic coefficients. The complexity of such power series is measured using a certain height function on the algebraic closure of the field of rational functions over Q. The paper includes a construction of this height function, following an idea of Kani. We apply the effective Weierstrass Division Theo...

Local zero estimates and effective division in rings of algebraic power series

We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a ring with some additional properties. To prove this result we show an effective Weierstrass Division Theorem and an effective solution to the Ideal Membership P...

Wedderburn Polynomials over Division Rings

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...

X iv : 0 70 6 . 35 15 v 1 [ m at h . R A ] 2 4 Ju n 20 07 Wedderburn Polynomials over Division Rings , II

A polynomial f(t) in an Ore extension K[t;S,D] over a division ring K is a Wedderburn polynomial if f(t) is monic and is the minimal polynomial of an algebraic subset of K. These polynomials have been studied in [LL5]. In this paper, we continue this study and give some applications to triangulation, diagonalization and eigenvalues of matrices over a division ring in the general setting of (S,D...