In information retrieval, Algebra Theory is one of significant tools of Retrieval Modeling. The models on the basis of Algebra overcome the fault that partial matching can not be implemented within Boolean Model, then become more and more popular. This article analyses the Vector Space Model based on Algebra, and expands the model: expresses the index terms with minterm in order to reflect the relationship between terms, uses singular value decomposition to present the semantic structure of documents. At last, makes the compare between these models.