Commutative Algebra: Volume I

A precise, fundamental study of commutative algebra, this largely self-contained treatment is the first in a two-volume set. Intended for advanced undergraduates and graduate students in mathematics, its prerequisites are the rudiments of set theory and linear algebra, including matrices and determinants.
The opening chapter develops introductory notions concerning groups, rings, fields, polynomial rings, and vector spaces. Subsequent chapters feature an exposition of field theory and class...