Basic properties of rings; ideals and quotient rings; ring homeomorphisms; polynomial rings; left and right modules; free modules; direct sums of modules; finitely generated modules over P.I.D. Artinian and Noetherian modules; completely reducible modules; tensor product of modules; bimodules; algebras and coalgebras.; projective and injective modules; primitive and semi-primitive rings; and the radical of a ring. Prerequisite: MAT 621.