All rings are assumed to be with unity, associative and non-commutative. The authors study the relation between the functor localization \(S^{-1}()\) and the homological functor \(\widehat{\mathrm{Ext}}^n_B(-1,\mathfrak{B})\). The main results of the paper is the next theorem.
Theorem. Let \(B\) be a finitely generated Noetherian \(A\)-algebra, \(S\) a central multiplicatively closed subset of \(B\) and \(\mathfrak{B}\) an (B-B)-bialgebra. Then there exists an isomorphism of left \(S^{-1}B\)-algebra, \(S^{-1}B \otimes_ B\widehat{\mathrm{Ext}}^n_B(\Omega_{B/A},\mathfrak{B})\cong \widehat{\mathrm{Ext}}^n_{S^{-1}B}(\Omega_{S^{-1}B/A},S^{-1}\mathfrak{B})\).