Additive subgroups of a module that are saturated with respect to a subset of the ring
Abstract
Let T T be a subset of a ring A A , and let M M be an A A -module. We study the additive subgroups F F of M M such that, for all x ∈ M x \in M , if t x ∈ F tx \in F for some t ∈ T t \in T , then x ∈ F x \in F . We call any such subset F F of M M a T T -factroid of M M , which is a kind of dual to the notion of a T T -submodule of M M . We connect the notion with the zero-divisors on M M , various classes of primary and prime ideals of A A
Fields of Study & Subjects
Rings
Modules
and Algebras
Commutative Algebra and Its Applications
Advanced Topics in Algebra
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 195–231
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Book chapter