A hermitian analogue of the Broecker-Prestel theorem

Details A hermitian analogue of the Broecker-Prestel theorem A hermitian analogue of the Broecker-Prestel theorem

2007-07-25

arxiv.org/abs/0707.3754v3

Indag. Math. (N.S.) 19 (2008), no. 3, 349-358

Mathematics

Rings and Algebras

Final pre-publication version

Scientific paper

10.1016/S0019-3577(09)00007-X

The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of pythagorean index at most two, and algebras over SAP and ED fields.

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