Ring hulls of extension rings

In this survey, we provide some results and examples on the behavior of the quasi-Baer and the right FI-extending right ring hulls. We focus on these ring hulls for various ring extensions including group ring extensions, full and triangular matrix ring extensions, and infinite matrix ring extensions. We also establish connections between the right FI-extending right ring hulls of semiprime homomorphic images of R and the subrings of eQ(R)e, where e = e(2) is an element of Q(R).