Products in categories of fractions and universal inversion of homomorphisms

Main result. If finite direct products exist in a category and the class of morphisms $\Sigma$ is such that the category of fractions $[\Sigma ^{-1}]$ and the canonical functor $\mathfrak K\to [\Sigma ^{-1}]$ preserves these products. Using this theorem analogues of the theory of matrix localization of rings are constructed for arbitrary varieties of universal algebras and for preadditive categories.