Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 249–254 (2014) 

COMPLETELY PSEUDOVALUATION RINGS AND THEIR EXTENSIONSVijay Kumar BhatSchool of Mathematics, SMVD University, Katra182320, IndiaAbstract: Recall that a commutative ring $R$ is said to be a pseudovaluation ring if every prime ideal of $R$ is strongly prime. We define a completely pseudovaluation ring. Let $R$ be a ring (not necessarily commutative). We say that $R$ is a completely pseudovaluation ring if every prime ideal of $R$ is completely prime. With this we prove that if $R$ is a commutative Noetherian ring, which is also an algebra over $\mathbb{Q}$ (the field of rational numbers) and $\delta$ a derivation of $R$, then $R$ is a completely pseudovaluation ring implies that $R[x;\delta]$ is a completely pseudovaluation ring. We prove a similar result when prime is replaced by minimal prime. Classification (MSC2000): 16S36; 16N40, 16P40 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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