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Ulrich ideals and modules†

Published online by Cambridge University Press:  10 September 2013

SHIRO GOTO ,
KAZUHO OZEKI ,
RYO TAKAHASHI ,
KEI-ICHI WATANABE  and
KEN-ICHI YOSHIDA
SHIRO GOTO
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan e-mail: [email protected]
KAZUHO OZEKI
Affiliation:
Department of Mathematical Science, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8512, Japan e-mail: [email protected]
RYO TAKAHASHI
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan / Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA e-mail: [email protected] URL: http://www.math.nagoya-u.ac.jp/~takahashi/
KEI-ICHI WATANABE
Affiliation:
Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-Ku, Tokyo 156-8550, Japan e-mails: [email protected]; [email protected]
KEN-ICHI YOSHIDA
Affiliation:
Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-Ku, Tokyo 156-8550, Japan e-mails: [email protected]; [email protected]
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Abstract

In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 1 , January 2014 , pp. 137 - 166
Copyright
Copyright © Cambridge Philosophical Society 2013 

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Footnotes

†

This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 20540050/22540047/22540054/23540059, JSPS Grant-in-Aid for Young Scientists (B) 22740008/22740026 and by JSPS Postdoctoral Fellowships for Research Abroad

References

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