Submodules having the same generalized prime ideal factorization
Commutative Algebra
2026-01-06 v2
Abstract
In our recent work, we introduced a generalization of the prime ideal factorization in Dedekind domains for submodules of finitely generated modules over Noetherian rings. In this article, we find conditions for the intersection of two submodules to have the same factorization as the submodules. We also find the relation between the factorizations of a submodule in an -module and the ideal in the ring and give a condition for their equality.
Cite
@article{arxiv.2311.01706,
title = {Submodules having the same generalized prime ideal factorization},
author = {K. R. Thulasi and T. Duraivel and S. Mangayarcarassy},
journal= {arXiv preprint arXiv:2311.01706},
year = {2026}
}