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arXiv · 2411.17581

TTF classes generated by silting modules

Alejandro Argudin-Monroy·Daniel Bravo·Carlos E. Parra
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Abstract

We study the conditions under which a TTF class in a module category over a ring is silting. Using the correspondence between idempotent ideals over a ring and TTF classes in the module category, we focus on finding the necessary and sufficient conditions for $R/I$ to be a silting $R$-module, and hence for the TTF class $\mathbf{Gen}(R/I)$ to be silting, where $I$ is an idempotent two-sided ideal of $R$. In our main result, we show that $R/I$ is a silting module whenever $I$ is the trace of a projective $R$-module. Furthermore, we demonstrate that the converse holds for a broad class of rings, including semiperfect rings.

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Alejandro Argudin-Monroy, Daniel Bravo, Carlos E. Parra. 2024-11-26. TTF classes generated by silting modules. https://arxiv.org/abs/2411.17581

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