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 the general setting of an Ore skew polynomial ring K[t,S,D].