Polynomial identity rings as rings of functions

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...

differential polynomial rings of triangular matrix rings

Polynomial functions on finite commutative rings

Every function on a nite residue class ring D=I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a nite commutative local ring with maximal ideal P of nilpotency N satisfying for all a; b 2 R, if ab 2 Pn then a 2 P k , b 2 P j with k + j min(n;N), we determine the number of functions (as...

On annihilator ideals in skew polynomial rings

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...