Normal bases for quadratic extensions
Charles Small · Pacific Journal of Mathematics · 1974
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 /c-modules; the free ones form a subgroup Q F (k) of Q(k).Among the free ones are some which admit a normal basis (definition recalled below); these form a subgroup Q NB {k).This paper studies the filtration 0 £ Q NB £ Q F £ Q.