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A power-associative algebra is a magma $(M, *)$ where the subalgebra generated by any element is associative. This can obviously be axiomatized by an infinite set of equational identities. Can it also be finitely axiomatized in first-order logic, preferably with only equational identities? I asked this question a while ago, in here, but I didn't receive a satisfactory answer.

user107952
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  • You wrote "I asked this question a while ago, but I didn't receive a satisfactory answer." Please include a link to this previous question, even if it's been deleted. – John Omielan Apr 18 '20 at 03:57
  • I do not know what "finitely axiomatizable" means, but if you mean "finite amount of relations", then for a field of $char=0$ the answer is positive. The general case, I believe, is an open problem. I will look for a reference. – AHandsomeAlien Apr 18 '20 at 04:22
  • Don't re-ask questions, even if you didn't get a good answer. Instead, if you want to call more attention to a question, you can offer a bounty. – Eric Wofsey Apr 18 '20 at 04:54

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