The radius of a subcategory of modules
The radius of a subcategory of modules
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DOI：
10.2140/ant.2014.8.141
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发表时间：
2011-11
影响因子：
1.3
通讯作者：
Hailong Dao;Ryo Takahashi
中科院分区：
文献类型：
--
作者：
Hailong Dao;Ryo Takahashi
We introduce a new invariant for subcategories X of finitely generated modules over a local ring R which we call the radius of X. We show that if R is a complete intersection and X is resolving, then finiteness of the radius forces X to contain only maximal Cohen‐Macaulay modules. We also show that the category of maximal Cohen‐Macaulay modules has finite radius when R is a Cohen‐Macaulay complete local ring with perfect coefficient field. We link the radius to many well-studied notions such as the dimension of the stable category of maximal Cohen‐Macaulay modules, finite/countable Cohen‐Macaulay representation type and the uniform Auslander condition.
