Ideals as generalized prime ideal factorization of submodules

2023/09/04 by Thulasi, K. R., Duraivel, T., Mangayarcarassy, S.
#13E05 #13E15 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13A05 #Secondary: 13A15

paper · doi:10.48550/arxiv.2309.01573

Abstract

For a submodule N of an R-module M, a unique product of prime ideals in R is assigned, which is called the generalized prime ideal factorization of N in M, and denoted as P_M(N). But for a product of prime ideals \mathfrakp₁ ⋯ \mathfrakp_n in R and an R-module M, there may not exist a submodule N in M with P_M(N) = \mathfrakp₁ ⋯ \mathfrakp_n. In this article, for an arbitrary product of prime ideals \mathfrakp₁ ⋯ \mathfrakp_n and a module M, we find conditions for the existence of submodules in M having \mathfrakp₁ ⋯ \mathfrakp_n as their generalized prime ideal factorization.

Related

• Product of prime ideals as factorization of submodules
• Submodules having the same generalized prime ideal factorization
• Strongly Prime Submodules
• Prime M-Ideals, M-Prime Submodules, M-Prime Radical and M-Baer's Lower\n Nilradical of Modules
• Generalizations of prime submodules over non-commutative rings