# Minimal prime ideals of $\sigma(*)$-rings and their extensions

Bhat, V. K. (2013) Minimal prime ideals of $\sigma(*)$-rings and their extensions. Armenian Journal of Mathematics, 5 (2). pp. 98-104. ISSN 1829-1163

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## Abstract

Let $R$ be a right Noetherian ring which is also an algebra over $\mathbb{Q}$ ($\mathbb{Q}$ the field of rational numbers). Let $\sigma$ be an automorphism of R and $\delta$ a $\sigma$-derivation of $R$. Let further $\sigma$ be such that $a\sigma(a)\in P(R)$ implies that $a\in P(R)$ for $a\in R$, where $P(R)$ is the prime radical of $R$. In this paper we study minimal prime ideals of Ore extension $R[x;\sigma,\delta]$ and we prove the following in this direction: Let $R$ be a right Noetherian ring which is also an algebra over $\mathbb{Q}$. Let $\sigma$ and $\delta$ be as above. Then $P$ is a minimal prime ideal of $R[x;\sigma,\delta]$ if and only if there exists a minimal prime ideal $U$ of $R$ with $P = U[x;\sigma,\delta]$.

Item Type: Article Ore extension, automorphism, derivation, minimal prime 16-xx Associative rings and algebras 457 Prof. Vijay Kumar Bhat 08 Jan 2014 11:33 08 Jan 2014 11:33

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