Abstract. The paper establishes some interrelations between a finite sequence of sets of mappings of an abstract set S to complete residue system of pairwise relatively prime elements of any Dedekind ring and corresponding sequence of sets of mappings of the set S to the complete residue system corresponding to the product of these elements. This interrelation is related to Leng’s isomorphic factor-rings theorem. A string model is presented, which is an interpretation of the investigated structures in the case of the ring of integers and of one-element set S. It is shown that the results can be applied to compute the number of combinatorial objects defined in terms of finite residue rings. Refs: 9 titles.

Keywords: Dedekind rings, mapping into complete residue systems, reversible matrices over finite rings, Chinese residue theorem.