The perspective-Schröder–Bernstein property for modules and abelian groups
Journal of Algebra and its Applications, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0219498828500090
- Dergi Adı: Journal of Algebra and its Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Bassian module/abelian group, Perspective module, Schröder–Bernstein property, subperspective module
- Gazi Üniversitesi Adresli: Evet
Özet
In this paper, we study modules and abelian groups for which any two subperspective direct summands are perspective. We say such modules satisfy the perspective-Schröder–Bernstein (PSB)-property. It is shown that if the modules in a class of modules A which is closed under taking isomorphisms and (finite) direct sums satisfy the PSB-property, then Kaplansky’s first test problem holds for the modules in A. It is also shown that some classes of modules (such as Dedekind-finite, semisimple and modules over division rings) satisfy the PSB property. We also consider more deeply the particular case of abelian groups. For example, it is shown that all divisible groups and all torsion-complete p-groups have the PSB-property as well as all algebraically compact groups. Finally, we verify that if the group G has finite rank and its p-torsion subgroups are direct sums of a divisible group and a bounded group, then G has the PSB-property. This class includes all of the groups that instantiate one of the various “Bassian properties”.