⊕-J-supplemented modules. (May 2020)

• Record Type: Journal Article
• Authors: Ali, Abdlkareem; Khalid, Wasan
• Is Part Of: Journal of physics. Volume 1530(2020)
• Publication Date: 2020-05
• Subjects: ⊕-J-supplemented modules -- weakly ⊕-J-supplemented modules -- cofinitely ⊕-J-supplemented modules -- cofinitely weak ⊕-J-supplemented modules; Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1530/1/012056
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: Let R be an associative ring with identity and let M be a unitary left R-module. In this paper, we introduce a ⊕-Jacobson-supplemented module (for short ⊕-J-supplemented), as a generalization of J-supplemented module. We state the main properties of a ⊕-J-supplemented modules and supplying by examples and remarks for these module and several properties of this modules are given. Also we introduce weakly ⊕-J-supplemented modules and give a characterization of weakly ⊕-J-supplemented modules a conditions under which the direct sum of weakly ⊕-J-supplemented modules is weakly ⊕-J-supplemented are given. We define a cofinitely ⊕-J-supplemented modules (for short, cof-⊕-J-supplemented) and some type of modules that are related to cof-⊕-J-supplemented module and prove properties of this type of modules. Also we discuss the relation between them with examples and remarks.