Submodules having the same generalized prime ideal factorization

Articles in Press

Document Type : Research Paper

Authors

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

2 Department of Mathematics, Puducherry Technological University, Pondicherry, India.

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 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.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 01 May 2025

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