The cohomology algebra of polyhedral product spaces

In this paper, we compute the integral singular cohomology ring of homology split polyhedral product spaces and the singular cohomology algebra over a field of polyhedral product spaces. As an application, we give two polyhedral product spaces Z(K;X1,A1)Z(K;X1,A1) and Z(K;X2,A2)Z(K;X2,A2) such that the cohomology homomorphisms ik⁎:H⁎(Xk)→H⁎(Ak) induced by the inclusions are the same, but the cohomology rings of the two polyhedral product spaces are not isomorphic.