NONCOMMUTATIVE PROJECTIVE SCHEMES

An analogue of the concept of projective scheme is defined for noncommutative N-graded algebras using the quotient category C of graded right A-modules module its full subcategory of torsion modules. We define proj A = (C, A, s), where A is the object corresponding to the module A(A), and s is the autoequivalence defined by the shift of degrees. The triples equivalent to proj A for a right noetherian graded algebra A are characterized in terms of a condition chi on extensions. (C) 1994 Academic Press, Inc.