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Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras

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Are there any central simple algebras admitting a standard basis?

Are there any central simple algebras admitting a standard basis? By a standard basis I mean a normal basis that has a cyclic property generalizing that of the familiar basis $1, i, j, k$ for Quaterni …
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