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Let $R$ be a ring, $n$ a fixed non-negative integer, $𝒲 ℐ$ the class of all left $R$ -modules with weak injective dimension at most $n$ , and $𝒲 ℱ$ the class of all right $R$ -modules with weak flat dimension at most $n$ . Using left (right) $𝒲 ℐ$ -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that $- \otimes -$ is right balanced on $ℳ_{R} \times_{R} ℳ$ by $𝒲 ℱ \times 𝒲 ℐ$ , and investigate the global right $𝒲 ℐ$ -dimension of $_{R} ℳ$ by right derived functors of $\otimes$ .

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Rad-supplemented modules

Relative cohomolgy of groups.

Relative cyclic homology and the Bass conjecture.

Relative derived functors and the homology of groups

Relative EXT groups of Abelian categories

Relative homological categories.

Relative weak derived functors

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