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

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Abstract

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.

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Funding

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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Authors and Affiliations

  1. Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki, 214-8571, Japan

    Shiro Goto

  2. Department of Mathematics and Informatics, Graduate School of Science and Technology, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Ryotaro Isobe & Shinya Kumashiro

Authors
  1. Shiro Goto
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  2. Ryotaro Isobe
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  3. Shinya Kumashiro
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Correspondence to Shinya Kumashiro.

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Goto, S., Isobe, R. & Kumashiro, S. The Structure of Chains of Ulrich Ideals in Cohen-Macaulay Local Rings of Dimension One. Acta Math Vietnam 44, 65–82 (2019). https://doi.org/10.1007/s40306-018-0283-y

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  • DOI: https://doi.org/10.1007/s40306-018-0283-y

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