Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 277283 (2008) 

Associated prime ideals of skew polynomial ringsV. K. BhatSchool of Applied Physics and Mathematics, SMVD University, P/o Kakryal, Katra, J and K, India  182301, email: vijaykumarbhat2000@yahoo.comAbstract: 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): 16XX; 16S36, 16P40, 16P50, 16U20 Full text of the article:
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