Submodules having the same generalized prime ideal factorization
نویسندگان
1 Department of Mathematics, Pondicherry University, Pondicherry, India.
2 Department of Mathematics, Pondicherry University, Pondicherry, India.
3 Department of Mathematics, Puducherry Technological University, Pondicherry, India.
doi
10.22034/as.2024.20819.1684چکیده
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 show 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 $N$ in an $R$-module $M$ and the ideal $\mathrm{Ann}(M/N)$ in the ring $R$ and give a condition for their equality.
