2 research outputs found
Ideals as generalized prime ideal factorization of submodules
For a submodule of an -module , a unique product of prime ideals in
is assigned, which is called the generalized prime ideal factorization of
in , and denoted as . But for a product of prime
ideals in and an
-module , there may not exist a submodule in with
. In
this article, for an arbitrary product of prime ideals and a module , we find conditions for the
existence of submodules in having as their generalized prime ideal factorization
P A PRIME EXTENSION FILTRATION OF MODULES
Abstract: In this article we introduce a filtration for modules namely, regular prime extension filtration, which exist for all finitely generated modules over Noetherian rings. We show that any two such filtrations of a module have same length