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Generation in Module Categories and Derived Categories of Commutative Rings

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Commutative Algebra

Abstract

Let R be a ring, and let M, N be R-modules. It is a natural question to ask whether or how one can build M out of N by iteration of fundamental operations such as direct sums, direct summands and extensions. It is possible to think of this question not only in module categories but also in derived categories. In this article we consider the question in the case where R is a commutative noetherian ring.

The author was partly supported by JSPS Grant-in-Aid for Scientific Research 19K03443

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Notes

  1. 1.

    The notation 〈−〉 here is only to simply explain this example, which is different from the one appearing in Definition 4.1.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Ryo Takahashi

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  1. Ryo Takahashi
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Correspondence to Ryo Takahashi .

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  1. Department of Mathematics, Cornell University, Ithaca, NY, USA

    Irena Peeva

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Takahashi, R. (2021). Generation in Module Categories and Derived Categories of Commutative Rings. In: Peeva, I. (eds) Commutative Algebra. Springer, Cham. https://doi.org/10.1007/978-3-030-89694-2_24

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