Idempotents and Units of Matrix Rings over Polynomial Rings

Differential Polynomial Rings of Triangular Matrix Rings

differential polynomial rings of triangular matrix rings

Polynomial Rings over Pseudovaluation Rings

Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x ∈ P for any P ∈ Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring. (2) Let R be a σ-divided ring such that x ∈ P for any P ∈ Spec(R[x,σ]). Then R[x,σ] is also a σ-divided ring. Let now R be a commutative Noetherian Q-algebra (Q i...

Gray Images of Constacyclic Codes over some Polynomial Residue Rings

Let  be the quotient ring    where  is the finite field of size   and  is a positive integer. A Gray map  of length  over  is a special map from  to ( . The Gray map   is said to be a ( )-Gray map if the image of any -constacyclic code over    is a -constacyclic code over the field   . In this paper we investigate the existence of   ( )-Gray maps over . In this direction, we find an equivalent ...

Diagonal Matrix Reduction over Refinement Rings

  Abstract: A ring R is called a refinement ring if the monoid of finitely generated projective R- modules is refinement.  Let R be a commutative refinement ring and M, N, be two finitely generated projective R-nodules, then M~N  if and only if Mm ~Nm for all maximal ideal m of  R. A rectangular matrix A over R admits diagonal reduction if there exit invertible matrices p and Q such that PAQ is...