Homological dimensions of complexes of R-modules
محورهای موضوعی : Applied Mathematics
N. Tayarzadeh
1
(Department of Mathematics, Islamic Azad University, Gachsaran branch,
Gachsaran, Iran.)
Esmaiel Hosseini
2
(Department of Mathematics, Islamic Azad University, Gachsaran branch,
Gachsaran, Iran.)
Sh. Niknejad
3
(Department of Mathematics, Islamic Azad University, Gachsaran Branch,
Gachsaran, Iran.)
کلید واژه: Cotorsion theory, Cotorsion dimension, Projective dimension,
چکیده مقاله :
Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti(F,X)= 0, whenever Ris n-perfect and i > n.
Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.
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