Acta Mathematica Vietnamica

, Volume 44, Issue 1, pp 65–82 | Cite as

The Structure of Chains of Ulrich Ideals in Cohen-Macaulay Local Rings of Dimension One

  • Shiro Goto
  • Ryotaro Isobe
  • Shinya KumashiroEmail author


This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of Ulrich ideals are closely explored. The specific cases where the rings are of minimal multiplicity and GGL rings are analyzed.


Cohen-Macaulay ring Gorenstein ring Generalized Gorenstein ring Canonical ideal Ulrich ideal Minimal multiplicity 

Mathematics Subject Classification (2010)

13H10 13H15 


Funding information

The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (C) 16K05112. The second and third authors were partially supported by Birateral Programs (Joint Research) of JSPS and International Research Supporting Programs of Meiji University.


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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 Mathematics, School of Science and TechnologyMeiji UniversityTama-kuJapan
  2. 2.Department of Mathematics and Informatics, Graduate School of Science and TechnologyChiba UniversityChibaJapan

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