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Valuation Rings in Ore Extensions

✍ Scribed by H.H Brungs; M Schröder

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
137 KB
Volume
235
Category
Article
ISSN
0021-8693

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✦ Synopsis

Extensions of valuation rings V of a skew field K are considered in the skew Ž . field F s K x, for a monomorphism of K. At least two such extensions exist if is an automorphism, but no extension may exist if is a monomorphism only. There exist extensions R Ž a. of V in F with xR Ž a. s aR Ž a. for every non-zero a in K if and only if V is invariant and is compatible with V.

📜 SIMILAR VOLUMES

Valuation ideals of order two in 2-dimen
Valuation ideals of order two in 2-dimensional regular local rings
✍ Sunsook Noh 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 233 KB

## Abstract Let __K__ be the quotient field of a 2‐dimensional regular local ring (__R, m__) and let __v__ be a prime divisor of __R__, i.e., a valuation of __K__ birationally dominating __R__ which is residually transcendental over __R__. Zariski showed that: such prime divisor __v__ is uniquely a