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Almost Gorenstein rings arising from fiber products

Part of: Local rings and semilocal rings General theory of categories and functors

Published online by Cambridge University Press:  10 July 2020

Naoki Endo ,
Shiro Goto  and
Ryotaro Isobe
Naoki Endo*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN47907, USA URL: https://www.math.purdue.edu/nendo/
Shiro Goto
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki214-8571, Japane-mail:[email protected]
Ryotaro Isobe
Affiliation:
Department of Mathematics and Informatics, Graduate School of Science and Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japane-mail:[email protected]
*
e-mail: [email protected]
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Abstract

The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show that the fiber product $R \times _T S$ of Cohen–Macaulay local rings R, S of the same dimension $d>0$ over a regular local ring T with $\dim T=d-1$ is an almost Gorenstein ring if and only if so are R and S. In addition, the other generalizations of Gorenstein properties are also explored.

Keywords

fiber productCohen–Macaulay ringGorenstein ringalmost Gorenstein ring

MSC classification

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13H15: Multiplicity theory and related topics 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 383 - 400
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

The first author was partially supported by JSPS Grant-in-Aid for Young Scientists 20K14299 and JSPS Overseas Research Fellowships. The second author was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 16K05112. The third author was partially supported by Grant-in-Aid for JSPS Fellows 20J10517.

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