University of Guilan Journal of Algebra and Related Topics 2345-3931 9 2 2021 12 01 Generalized Prime Ideal Factorization of Submodules 121 129 5305 10.22124/jart.2021.19497.1271 EN K. R. Thulasi Department of Mathematics, Pondicherry University, Puducherry, India. 0000-0002-2233-3039 T. Duraivel Department of Mathematics, Pondicherry University, Puducherry, India. S. Mangayarcarassy Department of Mathematics, Pondicherry Engineering College, Puducherry, India. Journal Article 2021 05 02 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. https://jart.guilan.ac.ir/article_5305_206ef4f7e0c845b978892a17192ecc73.pdf