000			02801nam a22002897a 4500
003			IIITD
005			20250428155119.0
008			250427b |||||||| |||| 00| 0 eng d
020			_a9783031569098
040			_aIIITD
082			_a512.24 _bBAN-C
100			_aBandini, Andrea
245			_aCommutative algebra through exercises _cby Andrea Bandini, Patrizia Gianni and Enrico Sbarra
260			_aSwitzerland : _bSpringer, _c©2024
300			_axi, 392 p. ; _c24 cm.
500			_aIncludes index
505			_tPart1 : Theory
505			_tPart 2 : Exercises
505			_tPart 3 : Proofs and solutions
520			_aThis book provides a first introduction to the fundamental concepts of commutative algebra. What sets it apart from other textbooks is the extensive collection of 400 solved exercises, providing readers with the opportunity to apply theoretical knowledge to practical problem solving, fostering a deeper and more thorough understanding of the subject. The topics presented here are not commonly found in a single text. Consequently, the first part presents definitions, properties, and results crucial for understanding and solving the exercises, serving also as a valuable reference. The second part contains the exercises and a section with "True or False?" questions, which serves as a valid self-assessment test. Considerable effort has been invested in crafting solutions that provide the essential details, aiming for a well-balanced presentation. We intend to guide students systematically through the challenging process of writing mathematical proofs with formal correctness and clarity. Our approach is constructive, aiming to illustrate concepts by applying them to the analysis of multivariate polynomial rings and modules over a principal ideal domain (PID) whenever feasible. Algorithms for computing these objects facilitate the generation of diverse examples. In particular, the structure of finitely generated modules over a PID is analyzed using the Smith canonical form of matrices. Furthermore, various properties of polynomial rings are investigated through the application of Buchberger’s Algorithm for computing Gröbner bases. This book is intended for advanced undergraduates or master’s students, assuming only basic knowledge of finite fields, Abelian groups, and linear algebra. This approach aims to inspire the curiosity of readers and encourages them to find their own proofs while providing detailed solutions to support their learning. It also provides students with the necessary tools to pursue more advanced studies in commutative algebra and related subjects.
650			_aMathematics
650			_aAlgebra
650			_aCommutative algebra
700			_aGianni, Patrizia
700			_aSbarra, Enrico
942			_cBK _2ddc
999			_c189951 _d189951