Assassins and torsion functors II

TL;DR

This paper explores the relationships between assassins and torsion functors in modules over commutative rings, providing criteria and examples related to ideals with specific properties.

Contribution

It introduces new criteria and results connecting assassins, torsion submodules, and ideals, especially idempotent or nil ideals, in commutative algebra.

Findings

Criteria for assassins and torsion functors in modules

Results on idempotent and nil ideals

Examples illustrating theoretical concepts

Abstract

Fairness and centredness of ideals in commutative rings, i.e., the relations between assassins and weak assassins of a module, its small or large torsion submodule, and the corresponding quotients, are studied. General criteria as well as more specific results about idempotent or nil ideals are given, and several examples are presented.