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October, 2019 Residually faithful modules and the Cohen–Macaulay type of idealizations
Shiro GOTO, Shinya KUMASHIRO, Nguyen Thi Hong LOAN
J. Math. Soc. Japan 71(4): 1269-1291 (October, 2019). DOI: 10.2969/jmsj/80398039

Abstract

The Cohen–Macaulay type of idealizations of maximal Cohen–Macaulay modules over Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of which is related to the theory of Ulrich modules, and the other one is related to the theory of residually faithful modules and closed ideals, developed by Brennan and Vasconcelos.

Funding Statement

The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (C), 16K05112. The first and second authors were partially supported by Bilateral Programs of JSPS and International Research Supporting Programs of Meiji University. The third was partially supported by International Research Supporting Programs of Meiji University, and funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2017.10.

Citation

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Shiro GOTO. Shinya KUMASHIRO. Nguyen Thi Hong LOAN. "Residually faithful modules and the Cohen–Macaulay type of idealizations." J. Math. Soc. Japan 71 (4) 1269 - 1291, October, 2019. https://doi.org/10.2969/jmsj/80398039

Information

Received: 18 April 2018; Revised: 6 August 2018; Published: October, 2019
First available in Project Euclid: 14 June 2019

zbMATH: 07174407
MathSciNet: MR4023308
Digital Object Identifier: 10.2969/jmsj/80398039

Subjects:
Primary: 13H10
Secondary: 13H15

Keywords: Cohen–Macaulay ring , Gorenstein ring , maximal Cohen–Macaulay module , maximal embedding dimension , residually faithful module , Ulrich module

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 4 • October, 2019
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