Abstract Algebra

GROUP THEORY.Introduction to Groups.Subgroups.Quotient Groups and Homomorphisms.Group Actions.Direct and Semidirect Products and Abelian Groups.Further Topics in Group Theory.RING THEORY.Introduction to Rings.Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.Polynomial Rings.MODULES AND VECTOR SPACES.Introduction to Module Theory.Vector Spaces.Modules over Principal Ideal Domains.FIELD THEORY AND GALOIS THEORY.Field Theory.Galois Theory.AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA.Commutative Rings and Algebraic Geometry.Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.Introduction to Homological Algebra and Group Cohomology.INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.Representation Theory and Character Theory.Examples and Applications of Character Theory.Appendices.Index.