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arXiv · 2102.12775

Constructive basic theory of central simple algebras

Thierry Coquand·Henri Lombardi·Stefan Neuwirth
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Abstract

We provide a constructive treatment of basic results in the theory of central simple algebras. One main issue is the fact that one starting result, Wedderburn's Theorem stating that a simple algebra is a matrix algebra over a skew field, is not constructively valid. We solve this problem by proving instead a dynamical version of this theorem. One can use this to give constructive proofs of basic results of the theory of central simple algebras, such as Skolem-Noether Theorem. We illustrate this development by giving an elementary constructive proof of a theorem of Becher (which is itself a consequence of a celebrated theorem of Merkurjev).

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Thierry Coquand, Henri Lombardi, Stefan Neuwirth. 2021-02-25. Constructive basic theory of central simple algebras. https://arxiv.org/abs/2102.12775

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