Algebra & Number Theory

The radius of a subcategory of modules

Hailong Dao and Ryo Takahashi

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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.

Article information

Algebra Number Theory, Volume 8, Number 1 (2014), 141-172.

Received: 14 July 2012
Revised: 10 August 2013
Accepted: 14 September 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C60: Module categories
Secondary: 13C14: Cohen-Macaulay modules [See also 13H10] 16G60: Representation type (finite, tame, wild, etc.) 18E30: Derived categories, triangulated categories

radius of subcategory resolving subcategory thick subcategory Cohen–Macaulay module complete intersection dimension of triangulated category Cohen–Macaulay representation type


Dao, Hailong; Takahashi, Ryo. The radius of a subcategory of modules. Algebra Number Theory 8 (2014), no. 1, 141--172. doi:10.2140/ant.2014.8.141.

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