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VALUATIONS OF k((X1,...,Xn)) WITH PREASSIGNED GROUP OF VALUES.
- Source :
-
Journal of Algebra & Its Applications . Dec2004, Vol. 3 Issue 4, p453-468. 16p. - Publication Year :
- 2004
-
Abstract
- Let Γ be a totally ordered abelian group of finite rational rank r. Consider s and n two non-negative integers with r+s≤n and denote by K a field. The main purpose of this paper is to construct a s-dimensional valuation v of the quotient field K((X1,...,Xn)) of the corresponding power series ring K[[X1,...,Xn]] such that v birrationally dominates K[[X1,...,Xn]] and has Γ as group of values. This is possible except for the case in which Γ=ℤ is the group of the integers, s=0, n≥2 and K does not admit an infinite algebraic extension. In this last case, we show that there does not exist such a valuation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH labelings
*GRAPH theory
*FINITE groups
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 3
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 15593661
- Full Text :
- https://doi.org/10.1142/S0219498804000976