Prime extension dimension of a module

Document Type : Research Paper

Authors

1 Department of Mathematics, Pondicherry University, Puducherry, India.

2 Department of Mathematics, Pondicherry Engineering College, Puducherry, India.

3 Department of Mathematics, Indira Gandhi Institute of Technology, Odisha, India.

Abstract

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 \mrpe.dA(M).
This dimension measures how far a module is from torsion freeness. We show for every submodule N of M, \mrpe.dA(N)≤\mrpe.dA(M) and \mrpe.dA(N)+\mrpe.dA(M/N)≥\mrpe.dA(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.

Keywords

Journal of Algebra and Related Topics
Volume 6, Issue 2
December 2018
Pages 97-106

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