Modules whose Lattice of Radical Submodules is Noetherian

Authors
Hosein Fazaeli Moghimi
Milad Hakimi Ghalesafa
University of Birjand
Abstract
In this paper, we investigate radical Noetherian modules as a collection of modules whose lattice of radical submodules is Noetherian. The collection of radical Noetherian modules contains both families of Noetherian and Artinian modules properly. We will show that the set of minimal prime submodules of a radical Noetherian modules is finite. Also a ring $R$ is called radical Noetherian, if $R$ is a radical Noetherian $R$-module. We will prove that a multiplication $R$-module $M$ is radical Noetherian if and only if $R/Ann(M)$ is a radical Noetherian. Moreover, we will give and prove analogs of Cohen and Hilbert basis theorems for radical Noetherian rings.
Keywords
Radical submodule
Radical Noetherian module
Radical Noetherian ring
Multiplication module
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