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Finitely silting comodules in quasi-finite comodule category

Qianqian Yuan; Hailou Yao — 2023

Czechoslovak Mathematical Journal

We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.

Characterizations of incidence modules

Naseer Ullah; Hailou Yao; Qianqian Yuan; Muhammad Azam — 2024

Czechoslovak Mathematical Journal

Let $R$ be an associative ring and $M$ be a left $R$ -module. We introduce the concept of the incidence module $I (X, M)$ of a locally finite partially ordered set $X$ over $M$ . We study the properties of $I (X, M)$ and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

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