On ideals of prime rings involving $n$-skew commuting additive mappings with applications

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 Identities with Additive Mappings in Rings

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

On Prime Ideals of Noetherian Skew Power Series Rings

We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...

Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings

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...