Acta Mathematica Vietnamica

, Volume 44, Issue 1, pp 207–212 | Cite as

Openness of the Regular Locus and Generators for Module Categories

  • Srikanth B. Iyengar
  • Ryo TakahashiEmail author


This work clarifies the relationship between the openness of the regular locus of a commutative Noetherian ring R and the existence of generators for the category of finitely generated R-modules, the corresponding bounded derived category, and for the singularity category of R.


Bounded derived category Generator Module category Regular locus Singularity category 

Mathematics Subject Classification (2010)

13D09 13B22 



The authors are grateful to Shiro Goto, Kazuhiko Kurano, and Jun-ichi Nishimura for valuable suggestions. Finally, the authors thank the referee for reading the paper carefully and giving helpful comments.

Funding Information

The first author was partially supported by the National Science Foundation, under grant DMS-1700985. The second author was partially supported by JSPS Grant-in-Aid for Scientific Research 16K05098 and JSPS Fund for the Promotion of Joint International Research 16KK0099.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  3. 3.Department of MathematicsUniversity of KansasLawrenceUSA

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