Rings, ideals, factor rings, homomorphisms, finite and infinite fields, polynomials and roots, field extensions, algebraic numbers, and applications, for example, to Latin squares, finite geometries, geometrical constructions, error-correcting codes. [Note: PMATH 345 may be substituted for PMATH 334 whenever the latter is a requirement in an Honours plan.] Prereq: MATH 235 or 245; Not open to General Mathematics students