Lectures on Injective Modules and Quotient Rings

Injective modules.- Essential extensions and the injective hull.- Quasi-Injective modules.- Radical and semiprimitivity in rings.- The endomorphism ring of a quasi-injective module.- Noetherian, artinian, and semisimple modules and rings.- Rational extensions and lattices of closed submodules.- Maximal quotient rings.- Semiprime rings with maximum condition.- Nil and singular ideals under maximum conditions.- Structure of noetherian prime rings.- Maximal quotient rings.- Quotient rings and direct products of full linear rings.- Johnson rings.- Open problems.