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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Embedding rational simple algebras in the real quaternions [duplicate]
Is there any way to embed a rational division algebra of dimension higher than 4 over its center in the real quaternions ?
I think not, but I cannot prove it.