RT - Journal Article
T1 - Modules whose Lattice of Radical Submodules is Noetherian
JF - khu-mmr
YR - 2024
JO - khu-mmr
VO - 10
IS - 2
UR - http://mmr.khu.ac.ir/article-1-3262-en.html
SP - 66
EP - 81
K1 - Radical submodule
K1 - Radical Noetherian module
K1 - Radical Noetherian ring
K1 - Multiplication module.
AB - 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.
LA eng
UL http://mmr.khu.ac.ir/article-1-3262-en.html
M3
ER -