Geodesic
On Some Extremal Varieties of Associative Algebras
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 542-558

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Suppose that $F$ is a field of prime characteristic $p$ and $\mathbf V_p$ is the variety of associative algebras over $F$ defined by the identities $[[x,y],z]=0$ and $x^p=0$ if $p>2$ and by the identities $[[x,y],z]=0$ and $x^4=0$ if $p=2$ (here $[x,y]=xy-yx$). As is known, the free algebras of countable rank of the varieties $\mathbf V_p$ contain non-finitely generated $T$-spaces. We prove that the varieties $\mathbf V_p$ are minimal with respect to this property. 
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     author = {E. A. Kireeva and A. N. Krasilnikov},
     title = {On {Some} {Extremal} {Varieties} of {Associative} {Algebras}},
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     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a5/}
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E. A. Kireeva; A. N. Krasilnikov. On Some Extremal Varieties of Associative Algebras. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 542-558. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a5/