Let 𝔄₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let 𝔖₂ be the subvariety of the variety 𝔄₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety 𝔄₃ ∩ 𝔖₂𝔖₂. Therefore we infer that 𝔄₃ ∩ 𝔖₂𝔖₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in 𝔄₃ ∩ 𝔖₂𝔖₂. It is worth mentioning that these results were announced in 1999 in works of the international conference "Loops’99" (Prague).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1072,
author = {Nicolae Ion Sandu},
title = {Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {24},
year = {2004},
pages = {5-30},
zbl = {1192.17017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1072}
}
Nicolae Ion Sandu. Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 5-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1072/
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