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On the classification of centrally finite alternative division rings satisfying algebraic closure conditions

2 Pith papers cite this work. Polarity classification is still indexing.

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2026 1 2024 1

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On the first-order theories of quaternions and octonions

math.AG · 2024-04-07 · unverdicted · novelty 6.0

Axiomatizes the first-order theories of quaternions and octonions over the ring language, characterizes models as algebras over real closed fields, proves model completeness without quantifier elimination, and describes algebraic sets arising from ordered polynomials.

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  • On the first-order theories of quaternions and octonions math.AG · 2024-04-07 · unverdicted · none · ref 6

    Axiomatizes the first-order theories of quaternions and octonions over the ring language, characterizes models as algebras over real closed fields, proves model completeness without quantifier elimination, and describes algebraic sets arising from ordered polynomials.