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On a Shirshov basis of relatively free algebras of complexity $n$
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 363-374 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Shirshov basis is a set of elements of an algebra $A$ over which $A$ has bounded height in the sense of Shirshov. A description is given of Shirshov bases consisting of words for associative or alternative relatively free algebras over an arbitrary commutative associative ring $\Phi$ with unity. It is proved that the set of monomials of degree at most $m^2$ is a Shirshov basis in a Jordan PI-algebra of degree $m$. It is shown that under certain conditions on $\operatorname{var}(B)$ (satisfied by alternative and Jordan PI-algebras), if each factor of $B$ with nilpotent projections of all elements of $M$ is nilpotent, then $M$ is a Shirshov basis of $B$ if $M$ generates $B$ as an algebra. Bibliography: 12 titles. 
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     title = {On {a~Shirshov} basis of relatively free algebras of complexity~$n$},
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A. Ya. Belov. On a Shirshov basis of relatively free algebras of complexity $n$. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 363-374. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a6/

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