Geodesic
On the multiplicative and $T$-space structure of the relatively free Grassmann algebra
Sbornik. Mathematics, Tome 200 (2009) no. 9, pp. 1299-1338

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We investigate the multiplicative and $T$-space structure of the relatively free algebra $F^{(3)}$ with unity corresponding to the identity $[[x_1,x_2],x_3]=0$ over an infinite field of characteristic $p>0$. One of the basic results is the decomposition of quotient $T$-spaces connected with $F^{(3)}$ into a direct sum of simple components. Also, the $T$-spaces under consideration are commutative subalgebras of $F^{(3)}$; thus, the structure of $F^{(3)}$ and its subalgebras is described as modules over these commutative subalgebras. Finally, we consider the specifics of the case $p=2$. Bibliography: 15 titles.
Keywords: $T$-space, $T$-ideal, $n$-word, canonical basis, relatively free Grassmann algebra. 
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     author = {A. V. Grishin and L. M. Tsybulya},
     title = {On the multiplicative and $T$-space structure of the relatively free {Grassmann} algebra},
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A. V. Grishin; L. M. Tsybulya. On the multiplicative and $T$-space structure of the relatively free Grassmann algebra. Sbornik. Mathematics, Tome 200 (2009) no. 9, pp. 1299-1338. http://geodesic.mathdoc.fr/item/SM_2009_200_9_a1/