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Gabriel Dimension for Graded Rings

Authors:	M J Asensio C Năstăsescu B Torrecillas

Institution:	(1) Departamento de Algebra y Análisis Matemático, Universidad de Almería, E04120 Almería, Spain;(2) Facultatea de Matematica, University of Bucharest, Str. Academiei 14, RO-70109 Bucharest 1, Romania

Abstract:	Using techniques of localization for Grothendieck categories with a family of projective generators, we show that for a graded ring R = ⊕_σ∈G R _σ with finite support if R _e has Gabriel dimension then $R\hbox{-}{\rm gr}$ has Gabriel dimension. Moreover, adding some lattice results, we prove that if $R\hbox{-}{\rm mod}$ has Gabriel dimension then $R\hbox{-}{\rm gr}$ also has Gabriel dimension. This research has been supported by grant MTM2005-3227 from MEC.

Keywords:	graded ring Grothendieck categories projective generators Gabriel dimension
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