TY  - BOOK
AU  - Ferretti,Andrea
TI  - Commutative algebra
T2  - Graduate studies in mathematics,
SN  - 9781470474348
U1  - 512.71 
PY  - 2023///
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Commutative algebra
KW  - Commutative rings
KW  - Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.)
KW  - Number theory -- Algebraic number theory: global fields -- Algebraic numbers; rings of algebraic integers
KW  - Commutative algebra -- Computational aspects and applications -- None of the above, but in this section
KW  - Number theory -- Instructional exposition (textbooks, tutorial papers, etc.)
KW  - Algebraic geometry -- Foundations -- Varieties and morphisms
N1  - Includes bibliographical references and index; Graduate students and researchers interested in commutative algebra
N2  - 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
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UR  - https://www.goodreads.com/book/show/205591591-commutative-algebra?from_search=true&from_srp=true&qid=3plBPyKBll&rank=1#CommunityReviews
ER  -