A Course in Modern Algebra

In this classic work, Hilton and Wu's unique approach brings the reader from the elements of linear algebra past the frontier of homological algebra. They describe a number of different algebraic domains, then emphasize the similarities and differences between them, employing the terminology of categories and functors. The first two chapters present the necessary material on set theory, group theory, and the tensor product of abelian groups. Chapter three develops the appropriate language for making comparisons and unifications, describing such concepts as category, functor, natural transformation, and duality. Chapter four presents the concept of a module as a generalization of that of an abelian group (and of a vector space). Chapter five looks at principal ideal domains, Noetherian rings, and unique factorization domains. Chapter six discusses semisimple rings. Chapter seven crosses the frontier into homological algebra, with discussion of the two most fundamenta