Diagonal equivalence of matrices over a finite local ring

Diagonal Similarity and Equivalence for Matrices

the cyclic products of matrices and diagonal similarity. In this paper we consider diagonal similarity for matrices, which may be infinite, and whose elements lie in a (possible non-commutative) group G with O. Let H be a subgroup of a group G and let A be an irreducible square matrix with entries in GO. In Theorem 3.4, we give necessary and sufficient conditions for the existence of a matrix B...

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices

Results on the simultaneous scaling of nonnegative matrices involving one sided inequalities are presented. These are applied to scalings involving two sided inequalities. The proofs are graph theoretic. The setting is generalized to matrices with elements in lattice ordered Abelian groups with 0.

Flows on graphs applied to diagonal similarity and diagonal equivalence for matrices

Three equivalence relations are considered on the set of n x n matrices with elements in Fo' an · abelian group with absorbing zero adjoined. They are the relations of diagonal similarity, diagonal equivalence, and restricted diagonal equivalence. These relations are usually considered for matrices with elements in a field, but only multiplication is involved. Thus our formulation in terms of a...