#### Vol. 286, No. 2, 2017

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Classifying resolving subcategories

### William Sanders

Vol. 286 (2017), No. 2, 401–438
##### Abstract

We use the theory of Auslander–Buchweitz approximations to classify certain resolving subcategories containing a semidualizing or a dualizing module. In particular, we show that if the ring has a dualizing module, then the resolving subcategories containing maximal Cohen–Macaulay modules are in bijection with grade consistent functions and thus are the precisely the dominant resolving subcategories.

##### Keywords
resolving subcategory, homological dimension, commutative rings
##### Mathematical Subject Classification 2010
Primary: 13D05, 13C60
Secondary: 18G20, 13C14