Geodesic
Characterizations of incidence modules
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1127-1144
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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, \EIN -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of \EIN -modules is closed under direct product and upper triangular matrix modules.
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, \EIN -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of \EIN -modules is closed under direct product and upper triangular matrix modules.
DOI : 10.21136/CMJ.2024.0092-24
Classification : 13C13, 16D70, 16D80, 16D99
Keywords: Ikeda Nakayama module; essential Ikeda Nakayama module; nil injective; nonsingular 
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Ullah, Naseer; Yao, Hailou; Yuan, Qianqian; Azam, Muhammad. Characterizations of incidence modules. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1127-1144. doi: 10.21136/CMJ.2024.0092-24

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