Homological dimensions of complexes of R-modules

محورهای موضوعی : Applied Mathematics

N. Tayarzadeh ¹ , Esmaiel Hosseini ² , Sh. Niknejad ³

1 - Department of Mathematics, Islamic Azad University, Gachsaran branch, Gachsaran, Iran.
2 - Department of Mathematics, Islamic Azad University, Gachsaran branch, Gachsaran, Iran.
3 - Department of Mathematics, Islamic Azad University, Gachsaran Branch, Gachsaran, Iran.

تاریخ دریافت : 1391/11/15 تاریخ پذیرش : 1392/05/31 تاریخ انتشار : 1394/02/11

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.

چکیده انگلیسی:

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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