Right essentially Baer and quasi-Baer modules

We introduce the notions of right essentially Baer and quasi-Baer properties in a general module theoretic setting. A module M is called right essentially (quasi) Baer if the right annihilator of a (two-sided) left ideal of EndR(M) is essential in a direct summand of M . In this paper we show that the endomorphism rings of a right essentailly Baer module is right essentially Baer if R is a devision ring. Also we show that every fully invariant submodule N of M is right essentially Baer module when M is qusi-injective, right essentially Baer module.