Generalized triangular matrix rings and the fully invariant extending property. (Q1414997)

A module \(M\) is called (`strongly' -- P. Goeters) `FI-extending' if very fully invariant submodule of \(M\) is essential in a (fully invariant) direct summand of \(M\). A ring with identity is called quasi-Baer if the right annihilator of every ideal is generated, as a right ideal, by an idempotent. Characterizations of the generalized triangular matrix rings which are right FI-extending, respectively, right strongly FI-extending are proved. Also quasi-Baer generalized triangular matrix rings are characterized. Some examples which illustrate and delimit the classes obtained are given in the last section.