SEMISIMPLE-CONTINUOUS MODULES
MISKOLC MATHEMATICAL NOTES, cilt.27, sa.1, ss.149-165, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 27 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.18514/mmn.2026.5059
- Dergi Adı: MISKOLC MATHEMATICAL NOTES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), East & Central Europe Database (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Sayfa Sayıları: ss.149-165
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
An R-module M is said to be a semisimple-continuous, if it is weak CS (i.e., every semisimple submodule of M is essential in a direct summand of M) and semisimple-direct injective (i.e., if A and B are isomorphic semisimple submodules of M such that A is a direct summand of M, then B is a direct summand of M). It is proved that any semisimple-continuous module is decomposed as a direct sum of a semisimple module and a module with square-free socle. We investigate when the finite exchange property implies full exchange property for the former class of modules. Moreover, we explore the notion of the semisimple-continuity for Abelian groups. We also characterize right Noetherian right V-rings in terms of semisimple-continuous modules. Examples are delimit our results. 2010 Mathematics Subject Classification: 16D10; 16D40; 16P20; 16P60