On the Schröder-Bernstein property for abelian groups

KOŞAN M. T., Truong Cong Q., Žemlička J.

Communications in Algebra, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/00927872.2024.2430401
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Absolute direct summand, C2 property, Schröder-Bernstein property
  • Gazi Üniversitesi Adresli: Evet

Özet

A right R-module M satisfies the Schröder-Bernstein property, if whenever direct summands, say N and K, of M are d-subisomorphic to each other (i.e. if N is isomorphic to a direct summand of K and K is isomorphic to a direct summand of N), then (Formula presented.). The module M is said to be ADS (Absolute Direct Summand) if for every decomposition (Formula presented.) and every complement A of S, we have (Formula presented.). We primarily show that the question, whether ADS abelian groups satisfying the Schröder-Bernstein property, has a positive answer. Then we consider a related problem on the property C2 (a group G is C2 if whenever A is a summand of G and B is a subgroup of G isomorphic to A, then B is also a summand of G) and we present several sufficient conditions of C2 abelian groups to satisfy the Schröder-Bernstein property.