The Proj Construction
نویسنده
چکیده
Definition 1. Let A be a ring. A graded A-algebra is an A-algebra R which is also a graded ring in such a way that if r ∈ Rd then ar ∈ Rd for all a ∈ A. That is, Rd is an A-submodule of R for all d ≥ 0. Equivalently a graded A-algebra is a morphism of graded rings A −→ R where we grade A by setting A0 = A,An = 0 for n > 0. A morphism of graded A-algebras is a morphism of A-algebras which preserves grade. Equivalently, this is a morphism of graded rings which is also a morphism of A-modules, or a morphism of graded rings R −→ S making the following diagram commute R // S
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