Algebraic Structures

Intended as an introductory text for a course in algebra at the graduate level, this book provides a concise and comprehensive approach to the subject. Apart from the basics on groups, rings, fields and modules, it offers many important topics in Galois theory, multilinear algebra representation theory of groups, ring and field extensions, commutative and local algebra, homological algebra, lie algebras, Clifford algebras and the theory of categories and functions. The text is almost self-contained, and may serve as a preparatory introduction to the algebraic methods in number theory and geometry as well. The reader only requires a basic knowledge in linear algebra, but should also bring along with him a good sense for abstraction and elegance in mathematical thinking. The text is enhanced by numerous concrete examples and exercises.