Test sets for factorization properties of modules
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 217-238.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property with respect to\ a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in dependence on the algebraic structure of the underlying ring R and on additional set-theoretic hypotheses. For R commutative noetherian of Krull dimension 0<d<∞, we show that the assertion 'projectivity is a factorization property with respect to a single epimorphism' is independent of ZFC + GCH. We also show that if R is any ring and there exists a strongly compact cardinal κ>|R|, then the category of all projective modules is κ-accessible.

Publié le :
DOI : 10.4171/rsmup/66
Classification : 16, 03 
@article{RSMUP_2020__144__217_0,
     author = {Jan \v{S}aroch and Jan Trlifaj},
     title = {Test sets for factorization properties of modules},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {217--238},
     volume = {144},
     year = {2020},
     doi = {10.4171/rsmup/66},
     mrnumber = {4186456},
     zbl = {1477.16003},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/66/}
}
TY  - JOUR
AU  - Jan Šaroch
AU  - Jan Trlifaj
TI  - Test sets for factorization properties of modules
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2020
SP  - 217
EP  - 238
VL  - 144
UR  - http://www.numdam.org/articles/10.4171/rsmup/66/
DO  - 10.4171/rsmup/66
LA  - en
ID  - RSMUP_2020__144__217_0
ER  - 
%0 Journal Article
%A Jan Šaroch
%A Jan Trlifaj
%T Test sets for factorization properties of modules
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2020
%P 217-238
%V 144
%U http://www.numdam.org/articles/10.4171/rsmup/66/
%R 10.4171/rsmup/66
%G en
%F RSMUP_2020__144__217_0
Jan Šaroch; Jan Trlifaj. Test sets for factorization properties of modules. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 217-238. doi : 10.4171/rsmup/66. http://www.numdam.org/articles/10.4171/rsmup/66/

Cité par Sources :