Geodesic
On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
Matematičeskie trudy, Tome 3 (2000) no. 2, pp. 146-170

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It is proven that there exists no algorithm deciding whether the variety $\mathrm{var}\Sigma$ is finitely based relative to an arbitrary recursive system of ring identities $\Sigma$. An infinite sequence is constructed of finitely based varieties of nonassociative rings $\mathfrak A_1\supset\mathfrak B_1\supset\mathfrak A_2\supset\mathfrak B_2 \supset\dotsb$ such that, for all $i$, the equational theory of $\mathfrak A_i$ is undecidable and the equational theory of $\mathfrak B_i$ is decidable. 
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     author = {V. Yu. Popov},
     title = {On {Some} {Algorithmic} {Problems} {Related} to {Varieties} of {Nonassociative} {Rings}},
     journal = {Matemati\v{c}eskie trudy},
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     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2000_3_2_a5/}
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V. Yu. Popov. On Some Algorithmic Problems Related to Varieties of Nonassociative Rings. Matematičeskie trudy, Tome 3 (2000) no. 2, pp. 146-170. http://geodesic.mathdoc.fr/item/MT_2000_3_2_a5/