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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 71, Pages 4501-4509
http://dx.doi.org/10.1155/S0161171203209418

Atomical Grothendieck categories

1Faculty of Mathematics, University of Bucharest, Bucharest 1 RO 70109, Romania
2Departmento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, Spain

Received 11 September 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Motivated by the study of Gabriel dimension of a Grothendieck category, we introduce the concept of atomical Grothendieck category, which has only two localizing subcategories, and we give a classification of this type of Grothendieck categories.