Finite presentation and purity in categories σ[M]

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

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Abstract

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 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
Depositing User:	Professor Mike Prest
Date Deposited:	22 May 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/283

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