Petrichkovich V. M.
Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1575-1578
It is shown that an adequate ring with nonzero Jacobson radical has a stable range 1. A class of matrices over an adequate ring with stable range 1 is indicated.
A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations
Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 860–862
We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent.
Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 644–649
Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 478–483
Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 195 - 200