MATH 541 Ring Theory

Ideals, Prime and Maximal Ideals, Nilradical and Jacobson Radical of a ring, The Socle of a ring, Simple and semisimple rings, Idempotents, Structure of semisimple rings: The Weddeburn-Artin Theorem, Local and semilocal rings, Semiperfect rings, Perfect rings, Semiregular rings, Regular rings, The ring of full linear transformations, Artinian and Noetherian rings, Quasi-Frobenius rings.