Serial factorizations of right ideals

2018/02/11 by Facchini, Alberto, Nazemian, Zahra
#16D70 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1802.03786

Abstract

In a Dedekind domain D, every non-zero proper ideal A factors as a product A=P₁^t₁⋯ P_k^t_k of powers of distinct prime ideals P_i. For a Dedekind domain D, the D-modules D/P_i^t_i are uniserial. We extend this property studying suitable factorizations A=A₁… A_n of a right ideal A of an arbitrary ring R as a product of proper right ideals A₁,…,A_n with all the modules R/A_i uniserial modules. When such factorizations exist, they are unique up to the order of the factors. Serial factorizations turn out to have connections with the theory of h-local Prüfer domains and that of semirigid commutative GCD domains.

Related

• Submodules having the same generalized prime ideal factorization
• Factoring Ideals in Prüfer Domains
• Radical factorization in higher dimension
• Intrinsic factorization of ideals in Dedekind domains
• Valuation Ideal Factorization Domains