Some properties of T-supplemented modules
Logic Journal of the IGPL, vol.34, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1093/jigpal/jzag004
- Journal Name: Logic Journal of the IGPL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Business Source Ultimate (EBSCO)
- Keywords: modules, radical, small submodules, supplemented modules
- Ondokuz Mayıs University Affiliated: Yes
Abstract
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.