Characterizations of incidence modules
摘要
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.