V. E. Voskresenskii, “On the question of the structure of the subfield of invariants of a cyclic group of automorphisms of the field <nobr>$\mathbf Q(x_1,\dots,x_n)$</nobr>”, Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 2,Pages <nobr>366

This article is cited in 10 papers

On the question of the structure of the subfield of invariants of a cyclic group of automorphisms of the field $\mathbf Q(x_1,\dots,x_n)$

V. E. Voskresenskii

Abstract: The subfield $L$ of the field $K=\mathbf Q(x_1,\dots,x_n)$ consisting of invariant functions relative to a cyclic permutation of the indeterminates is interpreted as the field of rational functions on a certain torus defined over $\mathbf Q$. On this basis, a necessary condition is derived for pure transcendence of $L$ over $\mathbf Q$ from which are obtained a number of counterexamples. A list is also given of fields $L$ which are purely transcendental over $\mathbf Q$.

UDC: 513.6

MSC: 20B35, 20B25, 26C15, 12F20

Received: 01.09.1969