Abelian groups with chain conditions up to isomorphism
Journal of Pure and Applied Algebra, cilt.230, sa.10, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 230 Sayı: 10
- Basım Tarihi: 2026
- Doi Numarası: 10.1016/j.jpaa.2026.108351
- Dergi Adı: Journal of Pure and Applied Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Academic Search Ultimate (EBSCO)
- Anahtar Kelimeler: Abelian group, Chain conditions, Iso-artinian, Iso-noetherian, Module
- Gazi Üniversitesi Adresli: Evet
Özet
For a module G over a ring R , the concepts of iso-noetherian and iso-artinian are studied. Particularly it is shown that iso-noetherian modules over perfect rings are noetherian and the rest of paper is devoted to the case where R=Z, so that G is an abelian group. If G is such a group with torsion T and A=G/T, it is shown that G has either property if and only if it splits as T⊕A where both T and A have the corresponding property. The torsion groups satisfying either property are completely characterized, and when A is a Butler group, a complete description of when it is either iso-noetherian or iso-artinian is given.