… , Takahashi [11] showed that in the category of finitely generated R-modules both Serre and
… we show that in finitely generated modules over a commutative Noetherian ring R these two …

… A right R-module is finitely embedded if it has finitely generated essential socle (see, eg, …
bounded noetherian rings by showing that every finitely generated finitely embedded module is …

… In this section we study the functor which assigns to a finitely generated module over a pullback
ring its maximal artinian submodule, as it relates to … Let R be a noetherian ring and I a Ž . …

… finitely generated modules and injective modules over fully bounded Noetherian rings.
Our … Specialized to finite algebras over commutative Noetherian rings, some of our results …

… On the other hand it is weak enough to have many models, including the ring of … Noetherian
ring is finitely generated. Therefore, if we want an ideal or submodule to be finitely generated…

… Noetherian modules, almost finitely generated (afg) modules, and T-Noetherian modules. …
In [1], Anderson and Dumitrescu introduce the definition of T-Noetherian rings and modules. …

… Finitely generated modules over a Noetherian ring Submodules of a finitely generated module
need not be finitely generated; this … finitely generated modules over Noetherian rings are …

… A module is called distributive (is said to be a chain module) if the lattice of all its submodules
is distributive (is a chain). Let a ring A be a finitely generated module … semi-Noetherian ring, …

… module and a module of finite length. In this note we investigate rings whose cyclic or finitely
generated right modules … (l -e)R and since (1 -e)R is a Noetherian ring we can suppose by …

… Noetherian. In [3; Prop. 3], Math's proves that every fe module over a commutative
Noetherian ring is Artinian. This implies that A has finite length over R/O : RA, and hence over R. …