![]() ![]() We prove for a family of rings including generalized Dedekind domains that a ring R is a div. In the paper under review, there are completely integrally closed domains, in particular Krull domains, characterized in terms of being divisorial multiplication rings with respect to a Gabriel topology. Recall that an R-module M is said to be a multiplication module relative to ℱ (an ℱ-multiplication module or a divisorial multiplication module) if for every ℱ-closed submodule N, there exists an ideal A≤R such that N=Cl ℱ M (AM). The formula AB=Cl ℱ R (AB) for any couple of ℱ-closed ideals A,B defines a multiplication in C ℱ (R). The set of all ℱ-closed submodules of M is denoted by C ℱ (M). If N=Cl ℱ M (N), then N is called ℱ-closed. If N is a submodule of M, the closure of N in M is the set Cl ℱ M (N)=. From the paper: Throughout this note every ring R is a commutative ring with an identity element and ℱ represents a Gabriel topology over R or its associated Gabriel filter. The elderly philosopher Pythagoras, one of the most powerful characters of his time, is about to choose a successor among the great masters when a series of. ![]()
0 Comments
Leave a Reply. |