منابع مشابه
Generic Extensions and Generic Polynomials for Semidirect Products
This paper presents a generalization of a theorem of Saltman on the existence of generic extensions with group A ⋊ G over an infinite field K, where A is abelian, using less restrictive requirements on A and G. The method is constructive, thereby allowing the explicit construction of generic polynomials for those groups, and it gives new bounds on the generic dimension. Generic polynomials for ...
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Let g(X) ∈ K(t1, . . . , tm)[X] be a generic polynomial for a group G in the sense that every Galois extension N/L of infinite fields with group G and K ≤ L is given by a specialization of g(X). We prove that then also every Galois extension whose group is a subgroup of G is given in this way. Let K be a field and G a finite group. Let us call a monic, separable polynomial g(t1, . . . , tm, X) ...
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The notion of a generic Picard-Vessiot extension with group G is equivalent to that of a generic linear differential equation for the same group.
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In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A H to each twisted algebra H obtained from a Hopf algebra H by twisting its product with the help of a cocycle α. The algebra A H is a flat deformation of H over a “big” central subalgebra B H and can be viewed as the noncommutative analogue of a versal torsor in the sense of Serre. After surveying the results...
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Let G be an observable subgroup of GLn. We produce an extension of differential commutative rings generic for Picard–Vessiot extensions with
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2000
ISSN: 0747-7171
DOI: 10.1006/jsco.2000.0387