TY - JOUR
ID - 3331
TI - Prime extension dimension of a module
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Duraivel, T.
AU - Mangayarcarassy, S.
AU - Premkumar, K.
AD - Department of Mathematics, Pondicherry University, Puducherry, India.
AD - Department of Mathematics, Pondicherry Engineering College, Puducherry, India.
AD - Department of Mathematics, Indira Gandhi Institute of Technology, Odisha, India.
Y1 - 2018
PY - 2018
VL - 6
IS - 2
SP - 97
EP - 106
KW - Prime submodules
KW - Primary decomposition
KW - Prime filtration and Regular prime extension filtration
DO - 10.22124/jart.2018.11232.1116
N2 - 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).
UR - https://jart.guilan.ac.ir/article_3331.html
L1 - https://jart.guilan.ac.ir/article_3331_8a5342e66d28b4c73dccff01968afa06.pdf
ER -