  Let $A$ be the quotient of a graded polynomial ring
$\mathbb{Z}[x_1,\cdots,x_m]\otimes\Lambda[y_1,\cdots,y_n]$ by an ideal
generated by monomials with leading coefficients 1. Then we constructed a
space~$X_A$ such that $A$ is isomorphic to $H^*(X_A)$ modulo torsion elements.
