Year: 2026
Type: preprint
Abstract: Let $R$ be a commutative ring and $Φ$ an inverse family of ideals with greatest proper member $\mathcal{L}$. We introduce and study $Φ$-reduced and $Φ$-coreduced modules, extending the corresponding notions for powers of a single ideal. We show that, on these classes of modules, the generalized torsion and completion functors associated with $Φ$ are determined by $\mathcal{L}$. We establish characterizations and closure properties of these modules and obtain a Greenlees-May type adjunction and a Matlis-Greenlees-May type characterization. When $Φ$ is a system of ideals, we further investigate the radicality of the generalized torsion functor and derive associated torsion theories on suitable Serre subcategories. These results provide a module-theoretic framework for studying generalized torsion and completion with respect to families of ideals.
Source: arXiv (Cornell University)
Authors: Luambano, Sholastica, Ssevviiri, David
Institutions: The University of Dodoma, Makerere University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214313010