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Rings with Canonical Reductions

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Abstract

We study the class of one-dimensional Cohen–Macaulay local rings with canonical reductions, i.e., admit canonical ideals which are reductions of the maximal ideals, show that it contains the class of almost Gorenstein rings, and study characterizations for rings obtained by idealizations or by numerical semigroup rings to have canonical reductions.

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Acknowledgements

I would like to thank the referee for her/his careful reading and helpful suggestions. The author thanks the Graduate School of Advanced Mathematical Sciences of Meiji University hosting him as a visitor and a member of Professor Goto research group. The author also thanks Raheleh Jafari for discussions on numerical semigroup rings.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

    Mehran Rahimi

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  1. Mehran Rahimi
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Correspondence to Mehran Rahimi.

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Communicated by Rahim Zaare-Nahandi.

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Rahimi, M. Rings with Canonical Reductions. Bull. Iran. Math. Soc. 46, 1801–1825 (2020). https://doi.org/10.1007/s41980-020-00360-2

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  • DOI: https://doi.org/10.1007/s41980-020-00360-2

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