Abstract
The aim of this paper is threefold: first, to prove that the endomorphism ring associated to a pure subring of a regular local ring is a noncommutative crepant resolution if it is maximal Cohen-Macaulay; second, to see that in that situation, a different, but Morita equivalent, noncommutative crepant resolution can be constructed by using Frobenius morphisms; finally, to study the relation between Frobenius morphisms of noncommutative rings and the finiteness of global dimension. As a byproduct, we will obtain a result on wild quotient singularities: If the smooth cover of a wild quotient singularity is unramified in codimension one, then the singularity is not strongly F-regular.
Original language | English |
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Pages (from-to) | 15-31 |
Number of pages | 17 |
Journal | Journal of Algebra |
Volume | 370 |
DOIs | |
Publication status | Published - 2012 Nov 15 |
Keywords
- Cohen-Macaulay modules
- Endomorphism rings
- Frobenius morphisms
- Global dimension
- Noncommutative crepant resolutions
- Quotient singularities
- Skew group rings
ASJC Scopus subject areas
- Algebra and Number Theory