Resultants, companion matrices, and Jacobson chains (Q1090729)

It is well known that the concept of a Jacobson chain plays an important role in the theory of canonical forms of a matrix over an arbitrary field. In this paper the author shows that the reduction using Jacobson chains is a special case of a polyproduct rule for companion matrices. In addition, the author analyzes in detail the block form of a certain ''fundamental'' Jacobson chain, which generates all other chains. As a by- product of the product rule, the author obtains also several new results relating companion matrices and resultants.