Open AccessShort modules and almost noetherian modules
Author(s) -
Gökhan Bilhan,
Patrick F. Smith
Publication year - 2006
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14980
Subject(s) - noetherian , mathematics , pure mathematics , noetherian ring , ring (chemistry) , discrete mathematics , finitely generated abelian group , algebra over a field , chemistry , organic chemistry
It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodule $N$, either $N$ or $M/N$ is Noetherian if and only if $M$ contains submodules $K \supseteq L$ such that $M/K$ and $L$ are Noetherian and $K/L$ is almost Noetherian.