Introduction to Abstract Algebra

MATH 55300


MATH 45300


Group theory: finite abelian groups, symmetric groups, Sylow theorems, solvable groups, Jordan-H-lder theorem. Ring theory: prime and maximal ideals, unique factorization rings, principal ideal domains, Euclidean rings, and factorization in polynomial and Euclidean rings. Field theory: finite fields, Galois theory, and solvability by radicals.