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Morphisms represented by monomorphisms with n-torsionfree cokernel

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Abstract

We introduce and study a new class of morphisms which includes morphisms represented by monomorphisms in the sense of Auslander and Bridger. As an application, we give not only an extension of Kato’s theorem on morphisms represented by monomorphisms, but also a common generalization of several results due to Auslander and Bridger that describe relationships between torsionfreeness and the grades of Ext modules.

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Acknowledgements

The author would like to thank his supervisor Ryo Takahashi for a lot of valuable discussions and advice. The author would like to express my gratitude to Kiriko Kato who made valuable suggestions and comments. The author also thanks the referee very much for his/her useful comments and suggestions.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Yuya Otake

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  1. Yuya Otake
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Correspondence to Yuya Otake.

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Otake, Y. Morphisms represented by monomorphisms with n-torsionfree cokernel. Algebr Represent Theor 26, 2891–2912 (2023). https://doi.org/10.1007/s10468-022-10192-9

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