$\mathbb T$-Spaces of $n$-Words in a Relatively Free Grassmann Algebra without Unit in Characteristic $2$

In the paper, we continue the study of the relatively free Grassmann algebra $\mathbb F^{(3)}$ without unit over an infinite field of characteristic $2$, which was initiated in previous works of the author. The main attention is paid here to the relationship between the $\mathbb T$-spaces of $n$-words, i.e., the $\mathbb T$-spaces generated by all monomials in $\mathbb F^{(3)}$ containing each of their variables with multiplicity $n$. The results of this note will enable one to form a more complete picture of possible inclusions between the $\mathbb T$-spaces of $r$- and $n$-words for $r>n$.