University of GuilanJournal of Algebra and Related Topics2345-39316220181201Prime extension dimension of a module97106333110.22124/jart.2018.11232.1116ENT. DuraivelDepartment of Mathematics, Pondicherry University, Puducherry, India.S. MangayarcarassyDepartment of Mathematics, Pondicherry Engineering College, Puducherry, India.K. PremkumarDepartment of Mathematics, Indira Gandhi Institute of Technology, Odisha, India.Journal Article20180905We have that for a finitely generated module $M$ over a Noetherian ring $A$ any two RPE filtrations of $M$ have same length.<br /> We call this length as prime extension dimension of $M$ and denote it as $mr{pe.d}_A(M)$.<br /> 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<br /> 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).https://jart.guilan.ac.ir/article_3331_8a5342e66d28b4c73dccff01968afa06.pdf