Geodesic
Cartan-Eilenberg projective, injective and flat complexes
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 151-167

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $R$ be an associative ring with identity and $\mathcal {F}$ a class of $R$-modules. In this article: we first give a detailed treatment of Cartan-Eilenberg $\mathcal {F}$ complexes and extend the basic properties of the class $\mathcal {F}$ to the class ${\rm CE}(\mathcal {F}$). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes, including coherent, Noetherian, von Neumann regular rings, $\rm QF$ rings, semisimple rings, hereditary rings and perfect rings.
DOI : 10.1007/s10587-016-0247-0
Classification : 18G10, 18G25, 18G35
Keywords: Cartan-Eilenberg projective complex; Cartan-Eilenberg injective complex; Cartan-Eilenberg flat complex 
@article{10_1007_s10587_016_0247_0,
     author = {Zhai, Xiaorui and Zhang, Chunxia},
     title = {Cartan-Eilenberg projective, injective and flat complexes},
     journal = {Czechoslovak Mathematical Journal},
     pages = {151--167},
     publisher = {mathdoc},
     volume = {66},
     number = {1},
     year = {2016},
     doi = {10.1007/s10587-016-0247-0},
     mrnumber = {3483230},
     zbl = {06587881},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0247-0/}
}
TY  - JOUR
AU  - Zhai, Xiaorui
AU  - Zhang, Chunxia
TI  - Cartan-Eilenberg projective, injective and flat complexes
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 151
EP  - 167
VL  - 66
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0247-0/
DO  - 10.1007/s10587-016-0247-0
LA  - en
ID  - 10_1007_s10587_016_0247_0
ER  - 
%0 Journal Article
%A Zhai, Xiaorui
%A Zhang, Chunxia
%T Cartan-Eilenberg projective, injective and flat complexes
%J Czechoslovak Mathematical Journal
%D 2016
%P 151-167
%V 66
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0247-0/
%R 10.1007/s10587-016-0247-0
%G en
%F 10_1007_s10587_016_0247_0
Zhai, Xiaorui; Zhang, Chunxia. Cartan-Eilenberg projective, injective and flat complexes. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 151-167. doi: 10.1007/s10587-016-0247-0

Cité par Sources :