We produce a description of Galois extensions with Galois group Q , QC, or 8 QQ, suitable for constructing generic polynomials.
Generic Extensions and Generic Polynomials
β Scribed by Arne Ledet
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 213 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0747-7171
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β¦ Synopsis
We prove that the existence of generic polynomials and generic extensions are equivalent over an infinite field.
π SIMILAR VOLUMES
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
## Abstract We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (__Ο__~1~ + 1)βgameβclosed forcings. PFA can be destroyed by a strongly (__Ο__~1~ + 1)βgameβclosed forcing but not by an __Ο__~2~βclosed. (Β© 2004 WILEYβVCH Verlag GmbH & Co.
Let q"pS'1 be a power of a prime p, and let k O be an over"eld of GF(q). Let m'0 be an integer, let J\* be a subset of +1, 2 , m,, and let E\* KO (>)"> qK # HZ( \* X H >O K\H where the X H are indeterminates. Let J ? be the set of all m! where is either 0 or a divisor of m di!erent from m. Let s(ΒΉ)"