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Characterizations of Ding Injective Complexes

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Abstract

Let R be a ring and X a chain complex of R-modules. It is proven that if each term \(X_i\) is Ding injective in R-Mod for all \(i\in \mathbb {Z}\), and there exists an integer k such that each \(\mathrm{Z}_iX\) is Ding injective in R-Mod for all \(i\ge k\), then X is Ding injective in \(\mathrm{Ch}(R)\). If R is a left coherent ring, then a chain complex X is Ding injective if and only if each term \(X_i\) is Ding injective in R-Mod for all \(i\in \mathbb {Z}\).

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Gang Yang

  2. Universidad de Murcia, 30100, Murcia, Spain

    Sergio Estrada

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  1. Gang Yang
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  2. Sergio Estrada
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Correspondence to Sergio Estrada.

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Communicated by Shiping Liu.

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G. Yang is partially supported by NSF of China (Grant Nos. 11561039, 11761045, 11861055), NSF of Gansu Province (Grant Nos. 18JR3RA113, 17JR5RA091), and the Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University. S. Estrada is supported by the Grant MTM2016-77445-P and FEDER funds and by Grant 19880/GERM/15 from the Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia.

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Yang, G., Estrada, S. Characterizations of Ding Injective Complexes. Bull. Malays. Math. Sci. Soc. 43, 2385–2398 (2020). https://doi.org/10.1007/s40840-019-00807-8

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  • DOI: https://doi.org/10.1007/s40840-019-00807-8

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