TY - JOUR
AU - K. Mohammad Ali, Haibat
AU - E. Dahsh, Mohammad
PY - 2018
TI - W-Closed Submodule and Related Concepts
JF - Ibn AL- Haitham Journal For Pure and Applied Science; Vol 31 No 2 (2018)
DO - 10.30526/31.2.1955
KW -
N2 - Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.
UR - http://jih.uobaghdad.edu.iq/index.php/j/article/view/1955