Vol. 50, No. 2, 1974

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Normal bases for quadratic extensions

Charles Small

Vol. 50 (1974), No. 2, 601–611

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.

Mathematical Subject Classification 2000
Primary: 13B05
Received: 26 September 1972
Published: 1 February 1974
Charles Small