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Keywords:
Ikeda Nakayama module; essential Ikeda Nakayama module; nil injective; nonsingular
Ikeda Nakayama module; essential Ikeda Nakayama module; nil injective; nonsingular
Summary:
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.
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