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Inertial law of quadratic forms on modules over plural algebra

Marek Jukl (1995)

Mathematica Bohemica

Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].

Isometries of quadratic spaces

Eva Bayer-Fluckiger (2015)

Journal of the European Mathematical Society

Let k be a global field of characteristic not 2, and let f k [ X ] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the completions of k . This gives a partial answer to a question of Milnor.

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