Homological dimensions of complexes of R-modules

Subject Areas : 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.)

Received: 2013-02-03 Accepted : 2013-08-22 Published : 2015-05-01

Keywords: Cotorsion theory, Cotorsion dimension, Projective dimension,

Abstract :

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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