AU - Fazaeli Moghimi, Hosein
AU - Hakimi Ghalesafa, Milad
TI - Modules whose Lattice of Radical Submodules is Noetherian
PT - JOURNAL ARTICLE
TA - khu-mmr
JN - khu-mmr
VO - 10
VI - 2
IP - 2
4099 - http://mmr.khu.ac.ir/article-1-3262-en.html
4100 - http://mmr.khu.ac.ir/article-1-3262-en.pdf
SO - khu-mmr 2
ABĀ - 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.
CP - IRAN
IN - Department of Mathematics, University of Birjand, P. O. Box:97175-615
LG - eng
PB - khu-mmr
PG - 66
PT - S
YR - 2024