On modules in which every weak large closed submodule is a direct summand

M. H. Elbaroudy, M. A. Kamal, Manar E. Tabarak
2018 Applied Mathematical Sciences  
The concept of weak large extensions for modules is introduced here as a general case of the notion of large extensions. Some properties of large extensions hold true for weak large extensions, while some others need special types of modules (e.g. nonsingular modules), and special types of rings. Weak large extending modules (modules in which every W L-closed submodule is a direct summand) are also introduced here. We show that, as of the case of extending modules, the second singular submodule
more » ... singular submodule of a W L-extending module splits.
doi:10.12988/ams.2018.87107 fatcat:xxd3rcuaq5b25jbx2z3q7xd45u