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- W2787181105 abstract "The main purpose of this work is to give a constructive proof for a particular case of the no-name lemma. Let $G$ be a finite group, $K$ be a field, $L$ be a permutation $G$-lattice and $K[L]$ be the group algebra of $L$ over $K$. The no-name lemma asserts that the invariant field of the quotient field of $K[L]$, $K(L)^G$ is a purely transcendental extension of $K^G$. In other words, there exist $y_1, ldots , y_n$ which are algebraically independent over $K^G$ such that $K(L)^G cong K^G(y_1, ldots , y_n)$. We define elements $lbrace y_1, ldots, y_n rbrace subset K[L]^G$ with the desired properties, in the case when $G$ is the Galois group of a finite extension $mathrm{Gal}(K/F)$, and $L$ is a sign permutation $G$-lattice." @default.
- W2787181105 created "2018-02-23" @default.
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- W2787181105 date "2018-01-29" @default.
- W2787181105 modified "2023-09-27" @default.
- W2787181105 title "Algebraic Construction of Quasi-split Algebraic Tori" @default.
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