Generalized Prime Ideal Factorization of Submodules

Document Type : Research Paper

Authors

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

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

10.22124/jart.2021.19497.1271

Abstract

In this article, we introduce generalized prime ideal factorization for all proper submodules of a finitely generated module over a Noetherian ring. We show that the generalized prime ideal factorization of a product of two coprime ideals is the product of the generalized prime ideal factorization of the ideals. We find conditions under which the generalized prime ideal factorization of a product of prime ideals is equal to the product of the prime ideals. We show that if R is a Dedekind domain, the generalized prime ideal factorization of an ideal I in R is exactly the prime ideal factorization of I.

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