Nathan Jacobson's Basic Algebra I does not refer to basic, beginner algebra, but rather the first course one takes after linear algebra. This dense text provides both instruction and practice in understanding concepts from set theory, monoids and groups, rings, modules over a principal ideal domain, Galois Theory of equations, real polynomial equations and inequalities, metric vector spaces and the classical groups, algebras over a field, and lattices and Boolean algebras. Carefully explained proofs are also included. 499 pages, indexed, softcover.
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.
Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as Lie and Jordan algebras, lattices, and Boolean algebras. Exercises appear throughout the text, along with insightful, carefully explained proofs. Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication.
One of the world's leading researchers in abstract algebra, Nathan Jacobson (1910-95) taught at several prominent universities, including the University of Chicago, Johns Hopkins, and Yale.