Retracts of polynomial rings

Differential Polynomial Rings of Triangular Matrix Rings

Polynomial Retracts and the Jacobian Conjecture

Let K[x, y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra R of K[x, y] is called a retract if there is an idempotent homomorphism (a retraction, or projection) φ : K[x, y] → K[x, y] such that φ(K[x, y]) = R. The presence of other, equivalent, definitions of retracts provides several different methods of studying them, and brings together ideas from ...

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...

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...