caa a22 4500 606160825 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10468-014-9510-y doi (NATIONALLICENCE)springer-10.1007/s10468-014-9510-y Noncommutative (Crepant) Desingularizations and the Global Spectrum of Commutative Rings [Elektronische Daten] [Hailong Dao, Eleonore Faber, Colin Ingalls] In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We propose a notion of a NCCR over any commutative ring that appears weaker but generalizes all previous notions. Our results yield strong necessary and sufficient conditions for the existence of such objects in many cases of interest. We also give new examples of NCRs of curve singularities, regular local rings and normal crossing singularities. Moreover, we introduce and study the global spectrum of a ring R, that is, the set of all possible finite global dimensions of endomorphism rings of MCM R-modules. Finally, we use a variety of methods to compute global dimension for many endomorphism rings. Springer Science+Business Media Dordrecht, 2014 Noncommutative (crepant) resolutions nationallicence Rational singularities nationallicence Global spectrum nationallicence Endomorphism rings nationallicence Dao Hailong Department of Mathematics, University of Kansas, 66045-7523, Lawrence, KS, USA aut Faber Eleonore Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, M1A 1C4, Toronto, Ontario, Canada aut Ingalls Colin Department of Mathematics and Statistics, University of New Brunswick, E3B 5A3, Fredericton, NB, Canada aut Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 633-664 1386-923X 18:3<633 2015 18 10468 https://doi.org/10.1007/s10468-014-9510-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9510-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dao Hailong Department of Mathematics, University of Kansas, 66045-7523, Lawrence, KS, USA aut NATIONALLICENCE 700 1- Faber Eleonore Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, M1A 1C4, Toronto, Ontario, Canada aut NATIONALLICENCE 700 1- Ingalls Colin Department of Mathematics and Statistics, University of New Brunswick, E3B 5A3, Fredericton, NB, Canada aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 633-664 1386-923X 18:3<633 2015 18 10468