Year: 2021
Type: preprint
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).
Source: arXiv (Cornell University)
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3132562862