Generic extensions and generic polynomials for multiplicative groups
نویسندگان
چکیده
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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We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at q = 0 of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multi...
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Given an arbitrary irreducible polynomial f with rational coefficients it is difficult to determine the Galois group of the splitting field of that polynomial. When the roots of f are easy to calculate, there are a number of “tricks” that can be employed to calculate this Galois group. If the roots of f are solvable by radicals, for example, it is often easy to calculate by hand the Q-fixing au...
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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.06.034