  In this paper we investigate effects of a lattice dimension on strongly
correlated electronic systems at $T=0 K$. The model for numerical calculations
is formalized in terms of the integral equations which were obtained previously
for the half -- filled paramagnetic Hubbard model. The assumption that all
relevant functions of the system have a magnitude dependence of momentus
vectors makes ultimately possible treating a lattice dimension $D$ as an
external parameter. We here submit for consideration the number of doubly
occupied lattice sites, the electronic density of states, and the momentum
distribution in electronic occupation numbers at $D$=1, $D$=2, $D$=3
