A classical problem in homotopy theory asks which commutative graded algebra $A$ can be realized as the cohomology ring of a space. On one hand, any $\mathbb{Q}$-algebra $A$ is always isomorphic to the cohomology ring with rational coefficient of some space. On the other hand, the realization problem of $A$ as a cohomology ring with integral coefficient is very difficult. In this talk we will see how the polyhedral product construction can be applied to finding a space whose integral cohomology ring modulo torsion equals a polynomial ideal ring.