Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-18

(Weak) silting modules over tensor rings

Guoliang TANG, Jiaqun WEI

Received April 2, 2026. Published online September 21, 2026.

Abstract: Let $T_R(M)$ be a tensor ring, where $R$ is a ring and $M$ is an $N$-nilpotent $R$-bimodule. We give necessary and sufficient conditions under which a class of $T_R(M)$-modules is silting, cosilting, and weak silting. Additionally, we derive necessary conditions for general $T_R(M)$-modules to fall into these classes. Corresponding versions of these results are also obtained for tilting, cotilting, and ${\rm Tor}$-tilting modules. Applications are given to triangular matrix rings, which not only reproduce the earlier results in this direction, but also obtain some new conclusions.

Keywords: silting module; cosilting module; weak silting module; tensor ring

Classification MSC: 16D10, 16D80, 18G20

DOI: 10.21136/CMJ.2026.0133-26

PDF available at: Springer Institute of Mathematics CAS

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Affiliations: Guoliang Tang (corresponding author), Jiaqun Wei, School of Mathematical Sciences, Zhejiang Normal University, North Administration Building, 688 Yingbin Avenue, Jinhua 321004, P. R. China, e-mail: tangguoliang970125@163.com, weijiaqun5479@zjnu.edu.cn

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