The algebraic formalization of the use of hierarchical thematic classifiers in information retrieval depositories of documents was presented. The definitions of "rubricator ideals" and "multirubrics" on the root trees corresponding to hierarchical thematic classifiers were introduced. A lattice of rubricator ideals was constructed. Relations of thematic dominance, operations of lattice union and intersection of multirubrics were introduced, algorithms for their determination and calculation were presented. Therefore, a lattice of multirubrics was constructed that is isomorphic to the lattice of rubricator ideals. Isomorphism of lattice of multirubrics and boolean lattice of the set of leaf subsets of the root tree of the hierarchical thematic classifier was proved.