Finite presentation and purity in categories σ[M]

• Autorzy: Mike Prest , Robert Wisbauer
• Języki publikacji: EN

Abstrakty

EN

For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory 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 is 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 non-zero finitely presented objects.

Kategorie tematyczne

• 18E15: Grothendieck categories
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 99
• Numer: 2
• Strony: 189-202

Daty

wydano

2004

Twórcy

autor

Mike Prest

• Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

autor

Robert Wisbauer

• Mathematisches Institut der, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany

Identyfikatory

DOI

10.4064/cm99-2-4