Generalized Jordan forms of matrices over division rings

Abstract

Let [Formula: see text] be a division ring that is algebraic over its center [Formula: see text]. The aim of this paper is to describe certain classes of triangular matrices over [Formula: see text] that are similar to generalized Jordan forms, namely: (1) the class of finite triangular matrices, and (2) the class of infinite triangular matrices whose all diagonal entries, except possibly finitely many, belong to [Formula: see text].