Prime ideals in skew Laurent polynomial rings

Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings

Prime Radicals of Skew Laurent Polynomial Rings

Let R be a ring with an automorphism σ. An ideal I of R is σ-ideal of R if σ(I) = I. A proper ideal P of R is σ-prime ideal of R if P is a σ-ideal of R and for σ-ideals I and J of R, IJ ⊆ P implies that I ⊆ P or J ⊆ P . A proper ideal Q of R is σ-semiprime ideal of Q if Q is a σ-ideal and for a σ-ideal I of R, I2 ⊆ Q implies that I ⊆ Q. The σ-prime radical is defined by the intersection of all ...

Associated Prime Ideals of Skew Polynomial Rings

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

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...

A Dixmier-moeglin Equivalence for Skew Laurent Polynomial Rings

The work of Dixmier in 1977 and Moeglin in 1980 show us that for a prime ideal P in the universal enveloping algebra of a complex finite-dimensional Lie algebra the properties of being primitive, rational and locally closed in the Zariski topology are all equivalent. This equivalence is referred to as the Dixmier-Moeglin equivalence. In this thesis we will study skew Laurent polynomial rings of...