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020			_a9781470474348
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	0	_a512.71 _bFER-C
100	1		_aFerretti, Andrea
245	1	0	_aCommutative algebra
260			_aRhode Island : _bAmerican Mathematical Society, _c2023.
300			_axvii, 373p.
490			_aGraduate studies in mathematics, _vvolume 233 _x1065-7339 ;
504			_aIncludes bibliographical references and index.
520			_aThis 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.
521			_aGraduate students and researchers interested in commutative algebra.
650		0	_aCommutative algebra.
650		0	_aCommutative rings.
650		7	_aCommutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.).
650		7	_aNumber theory -- Algebraic number theory: global fields -- Algebraic numbers; rings of algebraic integers.
650		7	_aCommutative algebra -- Computational aspects and applications -- None of the above, but in this section.
650		7	_aNumber theory -- Instructional exposition (textbooks, tutorial papers, etc.).
650		7	_aAlgebraic geometry -- Foundations -- Varieties and morphisms.
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/gsm-233-toc.pdf?_gl=1*is8a8v*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxNTIyNC4wLjAuMA..
856			_3Index _uhttps://www.ams.org/bookstore/pspdf/gsm-233-index.pdf?_gl=1*54pw0y*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxNjU1MC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/205591591-commutative-algebra?from_search=true&from_srp=true&qid=3plBPyKBll&rank=1#CommunityReviews
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999			_c35058 _d35058