Precovers

Bican, Ladislav, and Torrecillas, Blas. "Precovers." Czechoslovak Mathematical Journal 53.1 (2003): 191-203. <http://eudml.org/doc/30768>.

@article{Bican2003,
abstract = {Let $\mathcal \{G\}$ be an abstract class (closed under isomorpic copies) of left $R$-modules. In the first part of the paper some sufficient conditions under which $\mathcal \{G\}$ is a precover class are given. The next section studies the $\mathcal \{G\}$-precovers which are $\mathcal \{G\}$-covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left $R$-modules. Especially, several sufficient conditions for the existence of $\sigma $-torsionfree and $\sigma $-torsionfree $\sigma $-injective covers are presented.},
author = {Bican, Ladislav, Torrecillas, Blas},
journal = {Czechoslovak Mathematical Journal},
keywords = {precover; cover; (pre)cover class of modules; hereditary torsion theory; relatively injective modules; precovers; covers; precover classes of modules; hereditary torsion theories; relatively injective modules; categories of modules},
language = {eng},
number = {1},
pages = {191-203},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Precovers},
url = {http://eudml.org/doc/30768},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Bican, Ladislav
AU - Torrecillas, Blas
TI - Precovers
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 191
EP - 203
AB - Let $\mathcal {G}$ be an abstract class (closed under isomorpic copies) of left $R$-modules. In the first part of the paper some sufficient conditions under which $\mathcal {G}$ is a precover class are given. The next section studies the $\mathcal {G}$-precovers which are $\mathcal {G}$-covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left $R$-modules. Especially, several sufficient conditions for the existence of $\sigma $-torsionfree and $\sigma $-torsionfree $\sigma $-injective covers are presented.
LA - eng
KW - precover; cover; (pre)cover class of modules; hereditary torsion theory; relatively injective modules; precovers; covers; precover classes of modules; hereditary torsion theories; relatively injective modules; categories of modules
UR - http://eudml.org/doc/30768
ER -