%0 Journal Article %T Generalized Prime Ideal Factorization of Submodules %J Journal of Algebra and Related Topics %I University of Guilan %Z 2345-3931 %A Thulasi, K. R. %A Duraivel, T. %A Mangayarcarassy, S. %D 2021 %\ 12/01/2021 %V 9 %N 2 %P 121-129 %! Generalized Prime Ideal Factorization of Submodules %K Prime submodules %K prime filtration %K regular prime extension filtration %R 10.22124/jart.2021.19497.1271 %X 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. %U https://jart.guilan.ac.ir/article_5305_206ef4f7e0c845b978892a17192ecc73.pdf