This note complements the
author’s paper in Journal of Pure and Applied Algebra, 2 (1972), in which a
computation is made of the functor which associates to each commutative ring k its
group Q(k) of quadratic extensions, where “quadratic extension of k” means “Galois
extension of k with respect to a group of order two”. In general, quadratic extensions
are rank two projective k-modules; the free ones form a subgroup QF(k) of Q(k).
Among the free ones are some which admit a normal basis (definition recalled
below); these form a subgroup QNB(k). This paper studies the filtration
0 ⊆ QNB⊆ QF⊆ Q.
