Homological aspects of semidualizing modules
Homological aspects of semidualizing modules
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DOI：
10.7146/math.scand.a-15121
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发表时间：
2007-03
影响因子：
0.5
通讯作者：
Ryo Takahashi;D. White
中科院分区：
文献类型：
--
作者：
Ryo Takahashi;D. White
我们研究了模的$C$-投射维度的概念，其中$C$是半对偶模。当$C=R$时，这恢复了标准射影维度。证明了有限$C~-射影维数的三个自然定义是一致的，并在此背景下研究了相对上同调模和绝对上同调模之间的关系。最后，我们证明了有限投射维模与有限$C$-投射维模之间的深层联系。同时，我们发展了关于内射维度和$C$-内射维度的对偶理论。
We investigate the notion of the $C$-projective dimension of a module, where $C$ is a semidualizing module. When $C=R$, this recovers the standard projective dimension. We show that three natural definitions of finite $C$-projective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results that demonstrate the deep connections between modules of finite projective dimension and modules of finite $C$-projective dimension. In parallel, we develop the dual theory for injective dimension and $C$-injective dimension.