Extensions of difference specializations
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- by Barbara Lando PDF
- Proc. Amer. Math. Soc. 79 (1980), 197-202 Request permission
Abstract:
Maximal difference specializations and difference places are defined. Let R be the domain of a difference specialization $\phi$ of a difference field K and $x \in K$. Then $\phi$ can be extended to a specialization $x \to 0$ if and only if $1 \notin [x]$. This result applies to give a condition on a polynomial for the extension of a specialization to its generic zero. In a slightly different direction, a necessary and sufficient condition for the extension of a specialization to a larger difference field is given.References
- Peter Blum, Complete models of differential fields, Trans. Amer. Math. Soc. 137 (1969), 309–325. MR 241396, DOI 10.1090/S0002-9947-1969-0241396-0
- Peter Blum, Extending differential specializations, Proc. Amer. Math. Soc. 24 (1970), 471–474. MR 258807, DOI 10.1090/S0002-9939-1970-0258807-0
- Richard M. Cohn, Difference algebra, Interscience Publishers John Wiley & Sons, New York-London-Sydeny, 1965. MR 0205987
- E. R. Kolchin, Differential algebra and algebraic groups, Pure and Applied Mathematics, Vol. 54, Academic Press, New York-London, 1973. MR 0568864
- S. D. Morrison, Extensions of differential places, Amer. J. Math. 100 (1978), no. 2, 245–261. MR 491640, DOI 10.2307/2373850
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 197-202
- MSC: Primary 12H10; Secondary 13J99, 13N05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565337-1
- MathSciNet review: 565337