Completely Pseudo-valuation Rings and Their Extensions
نویسندگان
چکیده
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 pseudovaluation 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 Q (the field of rational numbers) and δ a derivation of R, then R is a completely pseudo-valuation ring implies that R[x; δ] is a completely pseudo-valuation ring. We prove a similar result when prime is replaced by minimal prime.
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