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Dehomogenization of gradings to Zariskian filtrations and applications to invertible ideals

Authors: Hui Shi Li and Freddy Van Oystaeyen
Journal: Proc. Amer. Math. Soc. 115 (1992), 1-11
MSC: Primary 16W50; Secondary 16W60
MathSciNet review: 1081698
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Abstract: The method of dehomogenizing graded rings has been used successfully in algebraic geometry, e.g., a determinental ring is a dehomogenization of a Schubert cycle. We extend this method to noncommutative graded rings, dehomogenizing suitably graded rings to Zariski filtered rings and deriving, in a very elementary way, homological properties related to Auslander regularity and the Gorenstein property for noncommutative rings. As an application we study the lifting of such properties from a quotient modulo an invertible ideal.

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