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When is $ R \ltimes I$ an almost Gorenstein local ring?


Authors: Shiro Goto and Shinya Kumashiro
Journal: Proc. Amer. Math. Soc. 146 (2018), 1431-1437
MSC (2010): Primary 13H10; Secondary 13H05, 13H15
DOI: https://doi.org/10.1090/proc/13835
Published electronically: November 7, 2017
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Abstract: Let $ (R, \mathfrak{m}) $ be a Gorenstein local ring of dimension $ d > 0$ and let $ I$ be an ideal of $ R$ such that $ (0) \ne I \subsetneq R$ and $ R/I$ is a Cohen-Macaulay ring of dimension $ d$. There is given a complete answer to the question of when the idealization $ A = R \ltimes I$ of $ I$ over $ R$ is an almost Gorenstein local ring.


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Additional Information

Shiro Goto
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan
Email: shirogoto@gmail.com

Shinya Kumashiro
Affiliation: Department of Mathematics and Informatics, Graduate School of Science and Technology, Chiba University, Chiba-shi 263, Japan
Email: polar1412@gmail.com

DOI: https://doi.org/10.1090/proc/13835
Received by editor(s): March 17, 2017
Received by editor(s) in revised form: May 11, 2017
Published electronically: November 7, 2017
Additional Notes: The first author was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 25400051. Both authors are partially supported by JSPS Bilateral Programs (Joint Research) and International Research Supporting Program of Meiji University
Communicated by: Irena Peeva
Article copyright: © Copyright 2017 American Mathematical Society

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