ON ESSENTIAL PSEUDO P- INJECTIVE MODULE

A module is said to be an essential pseudo p-injective module if every monomorphism extends to , where , the set of all essential cyclic submodules of M. We establish several equivalent conditions for a module to be pseudo injective. We show that if a module has no proper essential submodule, then it is an essential Pseudo injective module. We prove that an essential pseudo injective module having no proper essential submodule is isomorphic to its direct summand. We also show that an essential submodule of an essential pseudo injective module is also essential pseudo injective and essential pseudo stable under certain conditions. Moreover, every essential pseudo stable submodule of an essential pseudo injective module, is also essential pseudo injective and intersection of any two invariant submodules of is an essential pseudo stable submodule of .