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9781470471279 Academic Inspection Copy

Commutative Algebra

  • ISBN-13: 9781470471279
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Andrea Ferretti
  • Price: AUD $347.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 28/02/2024
  • Format: Hardback (254.00mm X 178.00mm) 373 pages Weight: 272g
  • Categories: Algebra [PBF]Algebraic geometry [PBMW]
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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. 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.
Basics Finiteness conditions Factorization Computational methods Integral dependence Lattice methods Metric and topological methods Geometric dictionary Dimension theory Local structure Fields Bibliography Index of notation Index
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