Recently published studies have shown that Latent Semantic Indexing (LSI) plays an important role in content-based full text information retrieval of P2P system. However, it is a challenging problem to generate global consistent LSI structures in P2P systems because their nodes are self-organizing and their corpora are large, dynamic and distributed on different nodes. In this paper we propose a method for building LSI structures from distributed corpora. Our method is consisted with a network model for semantic information sampling and exchanging and a Reduced-Dimension-Representation (RDR)s merging algorithm. By the signal and noise subspace model, we also provide a theoretical justification that the RDR merging algorithm is sound. A simple numerical experiment shows that our RDR merging algorithm can keep query precision on an acceptable level.