GENERALIZED PRIME IDEAL FACTORIZATION OF SUBMODULES

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 a in r is exactly the prime ideal factorization of a.