On filtration of Clifford A-algebras and localization of A-modules

Abstract

Let (X;A) be an algebraized space. We consider sheaves of Clifford A-algebras (Clifford AX-algebras, for short) on X associated with arbitrary quadratic A-modules and study the the natural ltration of Clifford A-algebras. We show that for every A-algebra sheaf E, endowed with a regular ltration, one obtains a new graded A-algebra sheaf, denoted Gr(E), which turns out to be A-isomorphic to E.Finally, we also consider localization of A-modules at prime ideal subsheaves and at subsheaves induced by maximal ideals.

Key words: Clifford A-algebra, ltration of A-algebras, twisted tensor product, locally
algebraized space, prime ideal sheaf, Nakayama's lemma.