Abstract:
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
$r>n$.
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