COMPLETELY PSEUDO-VALUATION RINGS AND THEIR EXTENSIONS

Vijay Kumar Bhat

Abstract: Recall that a commutative ring $R$ is said to be a pseudo-valuation ring if every prime ideal of $R$ is strongly prime. We define a completely pseudo-valuation ring. Let $R$ be a ring (not necessarily commutative). We say that $R$ is a completely pseudo-valuation 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 pseudo-valuation ring implies that $R[x;\delta]$ is a completely pseudo-valuation 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)

• Compressed DVI file (20 kilobytes)
• Compressed PostScript file (368 kilobytes)
• PDF file (120 kilobytes)