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 a field that is equipped with a faithful G-action, and L a sign permutation G-lattice (see the Introduction for the definition). Then G acts naturally on the group algebra K[L] of L over K, and hence also on the quotient field K(L) = Q(K[L]). A well-known variant of the no-name lemma asserts that the invariant sub-field K(L)(G) is a purely transcendental extension of K-G. In other words, there exist which are algebraically independent over K-G such that K(L)(G) congruent to K-G(y(1), ..., y(n)). In this paper, we give an explicit construction of suitable elements y(1), ..., y(n).
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