Coherent polynomial rings over regular rings of finite index

On n-coherent rings, n-hereditary rings and n-regular rings

We observe some new characterizations of $n$-presented modules. Using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular 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...

Codes over finite quotients of polynomial rings

Codes over finite quotient of polynomial rings

Differential Polynomial Rings of Triangular Matrix Rings

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 ...