A GENERALIZATION OF SEMINOETHERIAN RINGS AND MODULES

We study those modules in which all submodules contain a nonzero submodule with Noetherian dimension less than or equal to \alpha where \alpha is the least ordinal number with this property, calling them modules that have enough \alpha-noetherians. Also, we study those modules in which any nonzero factor module contains a nonzero submodule with Noetherian dimension less than or equal to \alpha, where \alpha is the least ordinal number with this property, calling them \alpha-seminoetherians. Our work extends the results of Kourki and Tribak in Commu. Algebra (۲۰۲۲).

کلیدواژه ها:

Krull dimension ، Noetherian dimension ، seminoetherian modules ، enough noetherians