Goldie Conditions for Ore Extensions over Semiprime Rings

On Semiprime Right Goldie Mccoy Rings

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

PI ORE EXTENSIONS 3 1 Preliminaries

Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

Goldie Ranks of Skew Power Series Rings of Automorphic Type

Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B := A[[y;α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals.

Polynomial Ore Extensions of Baer and p.p.-Rings

Ore extensions of skew $pi$-Armendariz rings

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...