Finite presentation and purity in categories σ[M]

Mike Prest, and Robert Wisbauer. "Finite presentation and purity in categories σ[M]." Colloquium Mathematicae 99.2 (2004): 189-202. <http://eudml.org/doc/284915>.

@article{MikePrest2004,
abstract = {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.},
author = {Mike Prest, Robert Wisbauer},
journal = {Colloquium Mathematicae},
keywords = {finitely presented modules; pure embeddings; pure-injective objects; projective objects; locally finitely presented categories},
language = {eng},
number = {2},
pages = {189-202},
title = {Finite presentation and purity in categories σ[M]},
url = {http://eudml.org/doc/284915},
volume = {99},
year = {2004},
}

TY - JOUR
AU - Mike Prest
AU - Robert Wisbauer
TI - Finite presentation and purity in categories σ[M]
JO - Colloquium Mathematicae
PY - 2004
VL - 99
IS - 2
SP - 189
EP - 202
AB - 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.
LA - eng
KW - finitely presented modules; pure embeddings; pure-injective objects; projective objects; locally finitely presented categories
UR - http://eudml.org/doc/284915
ER -