Algebra & Number Theory
- Algebra Number Theory
- Volume 8, Number 1 (2014), 141-172.
The radius of a subcategory of modules
We introduce a new invariant for subcategories of finitely generated modules over a local ring which we call the radius of . We show that if is a complete intersection and is resolving, then finiteness of the radius forces to contain only maximal Cohen–Macaulay modules. We also show that the category of maximal Cohen–Macaulay modules has finite radius when 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.
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
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.ant/1513730137