The Functorial Topology With Discrete Class the Class of All Torsion Abelian Groups
Document Type
Peer-Reviewed Article
Publication Date
2025
Abstract
“Group” is understood to mean “abelian group”. Let Θ be the class of all torsion groups. Given any group A the family of subgroups { U ≤ A ∣ A ∕ U ∈ Θ } serves as a neighborhood base at 0 ∈ A defining a group topology on A in such a way that every group homomorphism is continuous. Thus the “ Θ -topology” does not add new structure to a group, i.e., A ≅ B as groups if and only if A and B are isomorphic as topological groups, but the topology raises new questions, and introduces related concepts and objects such as completions. The Θ -topology is thoroughly investigated in this paper.
DOI
10.1216/jca.2025.17.323
Recommended Citation
Dikranjan, D., Lewis, W., Loth, P., & Mader, A. (2025). The functorial topology with discrete class the class of all torsion abelian groups. Journal of Commutative Algebra, 17(3), 323-340. Doi: 10.1216/jca.2025.17.323
