Quadratic Pairs in Characteristic 2 and the Witt Cancellation Theorem
نویسنده
چکیده
We define the orthogonal sum of quadratic pairs and we show that there is no Witt cancellation theorem for this operation in characteristic 2. 1. Introduction. Quadratic pairs on central simple algebras were defined in [5]. They play the same role for quadratic forms as involutions for symmetric or skew-symmetric bilinear forms. In particular, they can be used to define twisted orthogonal groups in characteristic 2. In this paper, a notion of orthogonal sum of quadratic pairs is introduced on the model of Dejaiffe's orthogonal sum of involutions [2]. Moreover, an example is given to show that there is no cancellation for this operation.
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