%0 Journal Article
%T Prime extension dimension of a module
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Duraivel, T.
%A Mangayarcarassy, S.
%A Premkumar, K.
%D 2018
%\ 12/01/2018
%V 6
%N 2
%P 97-106
%! Prime extension dimension of a module
%K Prime submodules
%K Primary decomposition
%K Prime filtration and Regular prime extension filtration
%R 10.22124/jart.2018.11232.1116
%X We have that for a finitely generated module $M$ over a Noetherian ring $A$ any two RPE filtrations of $M$ have same length. We call this length as prime extension dimension of $M$ and denote it as $mr{pe.d}_A(M)$. This dimension measures how far a module is from torsion freeness. We show for every submodule (N) of (M), (mr{pe.d}_A(N)leqmr{pe.d}_A(M)) and (mr{pe.d}_A(N)+mr{pe.d}_A(M/N)geqmr{pe.d}_A(M)). We compute the prime extension dimension of a module using the prime extension dimensions of its primary submodules which occurs in a minimal primary decomposition of (0) in (M).
%U https://jart.guilan.ac.ir/article_3331_8a5342e66d28b4c73dccff01968afa06.pdf