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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Official URL: http://journals.impan.gov.pl/cm/Inf/99-2-4.html

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.

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