On hereditary reducibility of 2-monomial matrices over commutative rings

Abstract

A 2-monomial matrix over a commutative ring R is by definition any matrix of the form M(t, k, n) = Φ Ik 0 0 tIn−k

, 0 < k < n, where t is a non-invertible element of R, Φ the companion matrix to λ n − 1 and Ik the identity k × k-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility.