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1 - The behavior of homological dimensionsTheory of Approximation and Applications , Issue 1 , Year , Winter 2013Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-. Manuscript profile -
Article
2 - Homological dimensions of complexes of R-modulesTheory of Approximation and Applications , Issue 1 , Year , Winter 2015Let 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 applicatio MoreLet 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. Manuscript profile