Associated prime ideals of skew polynomial rings

V. K. Bhat

Abstract: In this paper, it has been proved that for a Noetherian ring $R$ and an automorphism $\sigma$ of $R$, an associated prime ideal of $R[x,\sigma]$ or $R[x,x^{-1}, \sigma]$ is the extension of its contraction to $R$ and this contraction is the intersection of the orbit under $\sigma$ 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 $\mathbb{Q}$-algebra ($\mathbb{Q}$ the field of rational numbers) and a derivation $\delta$ of $R$, an associated prime ideal of $R[x,\delta]$ is the extension of its contraction to $R$ and this contraction is an associated prime ideal of $R$.

Keywords: automorphism, associated prime, minimal prime, derivation, skew polynomial ring

Classification (MSC2000): 16-XX; 16S36, 16P40, 16P50, 16U20

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