arXiv:2611.03923v1 Announce Type: new Abstract: We prove that any variety of associative algebras over a Noetherian commutative ring with unity satisfying the identity x^3=0 is finitely based. This property has been known for the varieties satisfying the identity x^2=0. On the other hand, there are varieties satisfying the identity x^6=0 that are not finitely based.
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