Some properties of T-supplemented modules
Logic Journal of the IGPL, cilt.34, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1093/jigpal/jzag004
- Dergi Adı: Logic Journal of the IGPL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Business Source Ultimate (EBSCO)
- Anahtar Kelimeler: modules, radical, small submodules, supplemented modules
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
Let M be an R-module and T ≤ M. M is called a T-supplemented module if every submodule of M that contains T has a supplement in M. In this work, some properties of these modules are investigated. Let M be a T-supplemented R-module with T ≤ M. If T is (cofinitely) supplemented, then M is (cofinitely) supplemented. If T≪ M, then M is supplemented. Let M=M1+M2+...+Mn with Mi≤ M (i=1,2,...,n) and T=T1+T2+...+Tn with Ti≤ Mi (i=1,2,...,n). If Mi is Ti-supplemented for each i=1,2,...,n, then M is T-supplemented. Let M be an R-module and T≤ M. Then M is a T-supplemented if and only if M(Λ) is T(Λ)-supplemented for every finite index set Λ. Let f:M ⟶ N be an R-module epimorphism and T≤ M. If M is T-supplemented, then N is f (T)-supplemented. Let M be an R-module and T, V≤ M. If V is a supplement of a submodule U of M with T≤ U, then V is called a T-supplement submodule in M. Let M be an R-module and T≤ M. If every submodule of M that contain T is β* equivalent to a T-supplement submodule in M, then M is T-supplemented.