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Generic polynomials

✍ Scribed by Frank R DeMeyer


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
502 KB
Volume
84
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES


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We prove that the existence of generic polynomials and generic extensions are equivalent over an infinite field.

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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 βŠ† L and Gal(N/L) ≀ G arises as the splitting field of a suitable specialization g(Ξ» 1 , . . . , Ξ»m, X) with Ξ» i ∈ L. We discu

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We produce a description of Galois extensions with Galois group Q , QC, or 8 QQ, suitable for constructing generic polynomials.