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Valuations on Extensions of Weyl Skew Fields

✍ Scribed by Fred Van Oystaeyen; Luc Willaert

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
142 KB
Volume
183
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let k ; K be a finitely generated field extension of transcendence degree 1.

Ε½ . Ε½ .

Consider the corresponding extension

D D k ; D D K of skew fields of the first 1 1 Ε½ . Ε½ . Weyl algebra. We show that the D D k -valuations of D D K are in one-to-one 1 1 Ε½ . correspondence with the k-valuations of K. The intersection of the D D k -val-1 Ε½ . Ε½ . uation rings of D D K is not D D k as one would expect but a principal ideal 1 1

Ε½ . domain such that its quotient division ring is

0 is a finite-dimensional vector space over 1 Ε½ . D D k whose dimension equals the degree of D.

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