  We study linear and algebraic structures in sets of Dirichlet series with
maximal Bohr's strip. More precisely, we consider a set $\mathscr M$ of
Dirichlet series which are uniformly continuous on the right half plane and
whose strip of uniform but not absolute convergence has maximal width, i.e.,
$\frac{1}{2}$. Considering the uniform norm, we show that $\mathscr M$ contains
an isometric copy of $\ell_1$ (except zero) and is strongly
$\aleph_0$-algebrable. Also, there is a dense $G_\delta$ set such that any of
its elements generates a free algebra contained in $\mathscr M\cup \{0\}$.
Furthermore, we investigate $\mathscr{M}$ as a subset of the Hilbert space of
Dirichlet series whose coefficients are square-summable. In this case, we prove
that $\mathscr M$ contains an isometric copy of $\ell_2$ (except zero).
