Commutative Algebra Volume 1

This text covers commutative algebra, field theory, ideal theory, and Noetherian rings and Dedekind domains, with prerequisites including set theory and linear algebra. It is intended for advanced undergraduates and graduate students in mathematics.

Format: Paperback / softback
Length: 352 pages
Publication date: 31 December 2019
Publisher: Dover Publications Inc.

Commutative algebra is a fundamental branch of mathematics that focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. This text provides a comprehensive and rigorous study of these topics, covering material that has not been previously published in book form. It is intended for advanced undergraduates and graduate students in mathematics, with prerequisites including set theory and linear algebra, including matrices and determinants. The text begins with a review of the basic concepts of commutative algebra, such as rings, ideals, and homomorphisms, and then proceeds to explore more advanced topics such as polynomial rings, integral domains, and algebraic geometry. It also covers topics such as Noetherian rings, Dedekind domains, and the classification of finite groups. Throughout the text, numerous examples and exercises are provided to help students understand the concepts and apply them to real-world problems. Commutative algebra has numerous applications in various fields, including computer science, engineering, and economics. It is used to design and analyze algorithms, to study the properties of mathematical objects, and to solve complex problems. The text also provides a foundation for further study in algebra, such as algebraic number theory, algebraic geometry, and algebraic topology. In conclusion, commutative algebra is a crucial branch of mathematics that plays a vital role in many areas of science and engineering. This text provides a comprehensive and rigorous study of the field, with prerequisites that are accessible to advanced undergraduates and graduate students. It is recommended for anyone interested in pursuing a career in mathematics or related fields.
Commutative algebra is a fundamental branch of mathematics that focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. This text provides a comprehensive and rigorous study of these topics, covering material that has not been previously published in book form. It is intended for advanced undergraduates and graduate students in mathematics, with prerequisites including set theory and linear algebra, including matrices and determinants. The text begins with a review of the basic concepts of commutative algebra, such as rings, ideals, and homomorphisms, and then proceeds to explore more advanced topics such as polynomial rings, integral domains, and algebraic geometry. It also covers topics such as Noetherian rings, Dedekind domains, and the classification of finite groups. Throughout the text, numerous examples and exercises are provided to help students understand the concepts and apply them to real-world problems. Commutative algebra has numerous applications in various fields, including computer science, engineering, and economics. It is used to design and analyze algorithms, to study the properties of mathematical objects, and to solve complex problems. The text also provides a foundation for further study in algebra, such as algebraic number theory, algebraic geometry, and algebraic topology. In conclusion, commutative algebra is a crucial branch of mathematics that plays a vital role in many areas of science and engineering. This text provides a comprehensive and rigorous study of the field, with prerequisites that are accessible to advanced undergraduates and graduate students. It is recommended for anyone interested in pursuing a career in mathematics or related fields.

Weight: 480g
Dimension: 154 x 228 x 20 (mm)
ISBN-13: 9780486836614