Geodesic
On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
Matematičeskie trudy, Tome 3 (2000) no. 2, pp. 146-170 
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/
@article{MT_2000_3_2_a5,
     author = {V. Yu. Popov},
     title = {On {Some} {Algorithmic} {Problems} {Related} to {Varieties} of {Nonassociative} {Rings}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {146--170},
     year = {2000},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2000_3_2_a5/}
}
TY  - JOUR
AU  - V. Yu. Popov
TI  - On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
JO  - Matematičeskie trudy
PY  - 2000
SP  - 146
EP  - 170
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MT_2000_3_2_a5/
LA  - ru
ID  - MT_2000_3_2_a5
ER  - 
%0 Journal Article
%A V. Yu. Popov
%T On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
%J Matematičeskie trudy
%D 2000
%P 146-170
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/MT_2000_3_2_a5/
%G ru
%F MT_2000_3_2_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

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.