On the commutativity of the Clifford and “extension of scalars” functors

Abstract

We introduce sheaves of A-modules of fractions (or just A-modules of fractions), on a topological space X, with denominator a monoid-subsheaf S of A; as aside worth noting, we remark (Theorem 2.4) that there is an isomorphism between the functors S−1 and (S−1A)⊗_. Moreover, we discuss the classical problem related to the commutativity of the functors: Clifford functor Cl and algebra extension functor of the ground algebra K of a quadratic K-module(M,q). As a particular case, we show (Corollary 3.5) that given a sheaf A of algebras on a topological space X and S as above, the functor ClS−1A commutes with the functor S−1ClA.