## 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.

Item Type: | Article |
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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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