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ADDITIVE POLYNOMIALS AND THEIR ROLE IN THE MODEL THEORY OF VALUED FIELDS
- Source :
- Logic in Tehran ISBN: 9780367807108
- Publication Year :
- 2006
- Publisher :
- A K Peters/CRC Press, 2006.
-
Abstract
- We discuss the role of additive polynomials and p-polynomials in the theory of valued fields of positive characteristic and in their model theory. We outline the basic properties of rings of additive polynomials and discuss properties of valued fields of positive characteristic as modules over such rings. We prove the existence of Frobenius-closed bases of algebraic function fields F|K in one variable and deduce that F/K is a free module over the ring of additive polynomials with coefficients inK. Finally, we prove that every minimal purely wild extension of a henselian valued field is generated by a p-polynomial.
- Subjects :
- Discrete mathematics
Ring (mathematics)
Discrete orthogonal polynomials
010102 general mathematics
Free module
Field (mathematics)
01 natural sciences
Classical orthogonal polynomials
Difference polynomials
0103 physical sciences
Algebraic function
010307 mathematical physics
0101 mathematics
Mathematics
Variable (mathematics)
Subjects
Details
- ISBN :
- 978-0-367-80710-8
- ISBNs :
- 9780367807108
- Database :
- OpenAIRE
- Journal :
- Logic in Tehran ISBN: 9780367807108
- Accession number :
- edsair.doi.dedup.....8dc016dceb2d37fc6ffe062244eafbd4