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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 classical material concerning ideals and modules in arbitrary commutative rings, including detailed studies of direct sum decompositions. The final two chapters explore Noetherian rings and Dedekind domains. This work prepares readers for the more advanced topics of Volume II, which include valuation theory, polynomial and power series rings, and local algebra.
This Dover edition, first published in 2019, is an unabridged republication of the work originally published in the University Series in Higher Mathematics by D. Van Nostrand Company, Inc., Princeton, New Jersey, in 1958.
Description
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 classical material concerning ideals and modules in arbitrary commutative rings, including detailed studies of direct sum decompositions. The final two chapters explore Noetherian rings and Dedekind domains. This work prepares readers for the more advanced topics of Volume II, which include valuation theory, polynomial and power series rings, and local algebra.
This Dover edition, first published in 2019, is an unabridged republication of the work originally published in the University Series in Higher Mathematics by D. Van Nostrand Company, Inc., Princeton, New Jersey, in 1958.
