Essential-small submodules relative to an arbitrary submodule

2nd International Scientific Conference (Pure Sciences, Brilliant Creativity and Renewed Building)

Abbas, M.S.^1

Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq^1

关键词: Submodules;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/571/1/012030/pdf
DOI  :  10.1088/1757-899X/571/1/012030

来源: IOP

【 摘 要 】

Let R be an arbitrary ring and T a submodule of an R-module M. A submodule N is said to be Te-small in M, if for each essential submodule X of M, T ⊆ N + X implies that T ⊆ X. In this work we study this mentioned notion which is a generalization of the essential-small submodules as well as the T-small submodule. We use this notion to investigate T-essential radical of module, also to introduce generalized T-essential Hopfian modules.