Generalized Jordan forms of matrices over division rings (Q6655937)

The reviewed paper is pertained to the examination of the generalized Jordan forms of matrices over division rings. In fact, letting \(D\) be a division ring which is algebraic over its center \(Z(D)\), the target of the article under review is to characterize some special classes of triangular matrices with entries over \(D\) that are similar to generalized Jordan forms by considering the following two cases: (1) the class of finite triangular matrices; (2) the class of infinite triangular matrices whose all diagonal entries, except possibly finitely many of them, belong to \(Z(D)\).\N\NThe main result in the way of point (1) is Theorem 2.5. About the situation of infinite matrices described in point (2), the chief result is Theorem 3.2 which has a difficult proof that relies on a series of technical lemmas.\N\NThe paper is well-written, the obtained results are new, important and non-trivial, and thus the work contributes substantially on the expored subject being of interest for the experts in this branch.