  We extend the construction of moment-angle complexes to simplicial posets by
associating a certain T^m-space Z_S to an arbitrary simplicial poset S on m
vertices. Face rings Z[S] of simplicial posets generalise those of simplicial
complexes, and give rise to new classes of Gorenstein and Cohen--Macaulay
rings. Our primary motivation is to study the face rings Z[S] by topological
methods. The space Z_S has many important topological properties of the
original moment-angle complex Z_K associated to a simplicial complex K. In
particular, we prove that the integral cohomology algebra of Z_S is isomorphic
to the Tor-algebra of the face ring Z[S]. This leads directly to a
generalisation of Hochster's theorem, expressing the algebraic Betti numbers of
the ring Z[S] in terms of the homology of full subposets in S. Finally, we
estimate the total amount of homology of Z_S from below by proving the toral
rank conjecture for the moment-angle complexes Z_S.

Algebraic Topology;Commutative Algebra