Twisted multiplicative field invariants, Noether's problem, and galois extensions
TLDR
In this paper, it was shown that F(G) can be expressed as a kind of a-twisted invariant field when G is a nonsplit extension of G. The goal of this paper is to present this fact and then draw a series of conclusions using it.About:
This article is published in Journal of Algebra.The article was published on 1990-06-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Generic polynomial & Abelian extension.read more
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The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)
TL;DR: A survey of the Brauer group of G-invariants can be found in this paper, where the authors discuss the unramified Brauer groups of a function field and describe the work of Saltman and of Bogomolov.
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Retract rational fields
TL;DR: The notion of retract k-rationality was introduced by Saltman in the study of Noether's problem and other rationality problems as discussed by the authors, and the retract rationality of a field is investigated in this paper.
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Fields of definition for division algebras
TL;DR: In this article, the Brauer tensor product of two symbol algebras is defined over a rational extension of a finite-dimensional division algebra and the trace form of the algebra can be defined over any algebra of degree 4.
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Quasi-monomial actions and some 4-dimensional rationality problems
TL;DR: In this article, a quasi-monomial action is introduced, which is a generalization of the multiplicative group action, and the rationality problem of purely monomial group actions is studied.
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Negative solutions to three-dimensional monomial Noether problem
TL;DR: In this paper, the necessary and sufficient conditions for the coefficients to have a negative solution were derived by two criteria of irrationality using Galois cohomology, and the results were obtained by using two criteria for irrationality in the Noether problem.
References
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Book
Cohomology of Groups
TL;DR: In this paper, an advanced textbook introduces students to cohomology theory and no knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
Book
Linear algebraic groups
TL;DR: Conventions and notation background material from algebraic geometry general notions associated with algebraic groups homogeneous spaces solvable groups Borel subgroups reductive groups rationality questions are discussed in this paper.
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Separable algebras over commutative rings
Frank DeMeyer,Edward Ingraham +1 more
TL;DR: In this paper, the brauer group and central separable algebras were used to define the six-term exact sequence of the Brauer group, and they were shown to be the basis for Galois theory.
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La $R$-équivalence sur les tores
TL;DR: In this article, Gauthier-Villars implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).