Strongly Hollow R - Annihilator Lifting Modules and Strongly R - Annihilator (Hollow- Lifting) Modules
R-annihilator submodule
coessential submodule
hollow-lifting module
strongly hollow lifting module
Let R be a commutative ring with unity. Let W be an R-module, for K≤F, where F is a submodule of W and K is said to be R-annihilator coessential submodule of F in W (briefly R-a-coessential) if (denoted by K F in W). An R-module W is called strongly hollow -R-annihilator -lifting module (briefly, strongly hollow-R-a-lifting), if for every submodule F of W with hollow, there exists a fully invariant direct summand K of W such that K F in W. An R - module W is called strongly R - annihilator - ( hollow - lifting ) module ( briefly strongly R - a - ( hollow - lifting ) module ), if for every submodule F of W with R - a - hollow, there exists a fully invariant direct summand K of W such that K F in W.
