Balanced functors applied to modules
Balanced functors applied to modules
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DOI：
10.1016/0021-8693(85)90122-x
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发表时间：
1985-02
影响因子：
0.9
通讯作者：
E. Enochs;Overtoun M. G. Jenda
中科院分区：
文献类型：
--
作者：
E. Enochs;Overtoun M. G. Jenda
Cartan and Eilenberg [1, p. 961 call a functor T of several variables right balanced if T becomes an exact functor of the remaining variables when any covariant variable is replaced by an injective module or when any contravariant variable is replaced by a projective module. An advantage of knowing that a functor of several variables is right balanced is that the right derived functors can be computed using resolutions of any of the variables. When the functor Hom (-,-) is used this gives the familiar result that we get the same global dimension of a ring using injective resolutions or projective resolutions.The object of this paper is to modify and make a straightforward extension of this definition to the relative homological algebra situation formalized by Eilenberg and Moore in [21 (in fact, Eilenberg and Moore [2, p. 7) comment on a special case when Hom (-,-) is balanced without making the general definition). One application includes the interesting phenomenon of a difference in two between two definitions of the (relative) global dimension of a ring. This puts in perspective the fact, first noted in Bernecker [3], that certain full subcategories of the category of modules are reflective (or coreflective) only if the weak global dimension of the ring is at most two.
