Twisted polynomial rings satisfying a polynomial identity

Orderings and Valuations on Twisted Polynomial Rings

The real spectra of certain \twisted" polynomial algebras A over R are examined. In certain cases, including Weyl algebras and universal enveloping algebras of solvable Lie algebras, the stability indices of the residue spaces of Sper(A) are estimated. The results show that the Brr ocker-Scheiderer theory of minimal generation of constructible sets applies to Sper(A) in these cases. An attempt ...

Rings with a setwise polynomial-like condition

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

Differential Polynomial Rings of Triangular Matrix Rings

Representation Theory of Noetherian Hopf Algebras Satisfying a Polynomial Identity

A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelian-by-nite groups, nite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some common homological and representation-theoretic features of these algebras are described, with some indica...

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...