Commutative algebra
Material type:
TextSeries: Graduate studies in mathematics ; volume 233Publication details: Rhode Island : American Mathematical Society, 2023. Description: xvii, 373pISBN: 9781470474348Subject(s): Commutative algebra | Commutative rings | Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.) | Number theory -- Algebraic number theory: global fields -- Algebraic numbers; rings of algebraic integers | Commutative algebra -- Computational aspects and applications -- None of the above, but in this section | Number theory -- Instructional exposition (textbooks, tutorial papers, etc.) | Algebraic geometry -- Foundations -- Varieties and morphismsDDC classification: 512.71 Online resources: Table of Contents | Index | Reviews Summary: This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra.
The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra (Graduate Studies in Mathematics, Volume 234).
Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Book
|
SMS Library | 512.71 FER-C (Browse shelf(Opens below)) | Available | 25206 |
Browsing SMS Library shelves Close shelf browser (Hides shelf browser)
| 512.71 ATI-I Introduction to commutative algebra | 512.71 BEC-G Grobner bases: a computational approach to commutative algebra | 512.71 BRE-I Introduction to noncommutative algebra | 512.71 FER-C Commutative algebra | 512.71 FER-H Homological methods in commutative algebra | 512.71 KAN-C Course in commutative branch algebras(a) | 512.71 KRI-C Commutative algebra |
Includes bibliographical references and index.
This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra.
The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra (Graduate Studies in Mathematics, Volume 234).
Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.
Graduate students and researchers interested in commutative algebra.
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