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2006.110: Finite presentation and purity in categories σ[M]

2006.110: Mike Prest and Robert Wisbauer (2004) Finite presentation and purity in categories σ[M]. Colloq. Math., 99. pp. 189-202. ISSN 0010-1354

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For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcatgory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R are investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any nonzero finitely presented objects.

Item Type:Article
Subjects:MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MIMS number:2006.110
Deposited By:Professor Mike Prest
Deposited On:22 May 2006

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