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An indecomposable nonlocally finitely generated Grothendieck category with simple objects
- Source :
-
Journal of Algebra . Mar2009, Vol. 321 Issue 5, p1538-1545. 8p. - Publication Year :
- 2009
-
Abstract
- Abstract: A Grothendieck category is said to be locally finitely generated if the subobject lattice of every object in is compactly generated, or equivalently, if possesses a family of finitely generated generators. Every nonzero locally finitely generated Grothendieck category possesses simple objects. We shall call a Grothendieck category indecomposable if is not equivalent to a product of nonzero Grothendieck categories . In this paper an example of an indecomposable nonlocally finitely generated Grothendieck category possessing simple objects is constructed, answering in the negative a sharper form of a question posed by Albu, Iosif, and Teply in [T. Albu, M. Iosif, M.L. Teply, Dual Krull dimension and quotient finite dimensionality, J. Algebra 284 (2005) 52–79]. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 321
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 36140608
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2008.12.007