Amalgamation rings and the fully invariant extending property

Abstract

A module M is said to be FI-extending if every fully invariant submodule of M is essential in a direct summand of M. A ring R is right FI-extending if every ideal of R is right essential in an idempotent generated right ideal of R. A ring R is called quasi-Baer if the right annihilator of every ideal is generated as a right ideal, by an idempotent. In this paper we characterize the amalgamation ring , of the rings A, B along an ideal K of B with respect to a ring homomorphism , which is either right FI-extending or quasi-Baer.