Essential T- Weak Supplemented Modules

  • Firas sh. Fandi Department of Mathematics, College of Education for Pure Sciences, University Of Anbar, Ramadi, Iraq
  • Sahira M. Yaseen Department of Mathematics, College of Education for Pure Sciences, University Of Anbar, Ramadi, Iraq
Keywords: ET-small submodule, ET-lifting module, ET-H-supplemented, ET- weak – supplemented

Abstract

An R-module M is called ET-H-supplemented module if for each submodule X of M, there exists a direct summand D of M, such that T⊆X+K if and only if T⊆D+K, for every essential submodule K of M and T M. Also, let T, X and Y be submodules of a module M , then we say that Y is ET-weak supplemented of X in M if T⊆X+Y and (X⋂Y M. Also, we say that M is ET-weak supplemented module if each submodule of M has an ET-weak supplement in M. We give many characterizations of the ET-H-supplemented module and the ET-weak supplement. Also, we give the relation between the ET-H-supplemented and ET-lifting modules, along with the relationship between the ET weak -supplemented and ET-lifting modules.

Published
2020-05-17
How to Cite
FandiF. sh., & YaseenS. M. (2020). Essential T- Weak Supplemented Modules. Iraqi Journal of Science, 81-85. https://doi.org/10.24996/ijs.2020.SI.1.11