Abstract
Let K be an arbitrary field of characteristic zero with an absolute value on it. We show that if F and G are monic and normal polynomials of K[X] of the same degree with coefficients close enough to each other with respect to this absolute value, then the Galois groups of the splitting fields of F and G over K are isomorphic. We point out a quantitative result and discuss some special cases and related problems.
Original language | English (US) |
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Pages (from-to) | 2185-2191 |
Number of pages | 7 |
Journal | Communications in Algebra |
Volume | 47 |
Issue number | 5 |
DOIs | |
State | Published - May 4 2019 |
Keywords
- Diophantine approximation
- Galois groups
- polynomials
- splitting fields
ASJC Scopus subject areas
- Algebra and Number Theory