On the multiplicative and $T$-space structure of the relatively free Grassmann algebra

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 $p=2$.
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