On generic polynomials
β Scribed by Frank DeMeyer; Thomas McKenzie
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 91 KB
- Volume
- 261
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We prove that the existence of generic polynomials and generic extensions are equivalent over an infinite field.
We call a polynomial g(t 1 , . . . , tm, X) over a field K generic for a group G if it has Galois group G as a polynomial in X, and if every Galois field extension N/L with K β L and Gal(N/L) β€ G arises as the splitting field of a suitable specialization g(Ξ» 1 , . . . , Ξ»m, X) with Ξ» i β L. We discu
The exponential partial Bell polynomials are polynomials in an infinite number of variables x 1 , x 2 , . . . , and it is well-known that some special combinatorial sequences, e.g., Stirling numbers of both kinds, Lah numbers and idempotent numbers, can be obtained from the Bell polynomials. In this