Ukrainian Mathematical Bulletin

Volume 4, Issue 2, 2007 pp. 173-179.

On 2-primal Ore Extensions

Authors: Vijay K. Bhat
Author institution: School of Applied Physics and Mathematics, SMVD University, P/o Kakryal, Udhampur, J and K, India 182121 vijaykumarbhat2000@yahoo.com

Summary: Let $R$ be a ring, $\sigma$ an automorphism of $R$, and $\delta$ a $\sigma$-derivation of $R$. We define a $\delta$ property on $R$. We say that $R$ is a $\delta$-ring if $a\delta(a)\in P(R)$ implies $a\in P(R)$, where $P(R)$ denotes the prime radical of $R$. We ultimately show the following. Let $R$ be a Noetherian $\delta$-ring, which is also an algebra over $Q$, $\sigma$ and $\delta$ be as usual such that $\sigma(\delta(a))$ = $\delta(\sigma(a))$ for all $a\in R$ and $\sigma(P) = P$, $P$ any minimal prime ideal of $R$. Then $R[x,\sigma,\delta]$ is a $2$-primal Noetherian ring.

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