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Titlebook: Commutative Algebra through Exercises; Andrea Bandini,Patrizia Gianni,Enrico Sbarra Textbook 2024 The Editor(s) (if applicable) and The Au

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發(fā)表于 2025-3-21 17:47:47 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Commutative Algebra through Exercises
編輯Andrea Bandini,Patrizia Gianni,Enrico Sbarra
視頻videohttp://file.papertrans.cn/243/242221/242221.mp4
概述Comprehensive coverage: find the basic abstract concepts and their applications in a single easy-to-use text.Algorithmic insight: delve into the algorithmic aspects of commutative algebra and computin
叢書名稱UNITEXT
圖書封面Titlebook: Commutative Algebra through Exercises;  Andrea Bandini,Patrizia Gianni,Enrico Sbarra Textbook 2024 The Editor(s) (if applicable) and The Au
描述.This 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 titled 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.
出版日期Textbook 2024
關(guān)鍵詞Rings and ideals; Modules; Gr?bner bases; Primary decomposition; Localization; Multivariate polynomials; S
版次1
doihttps://doi.org/10.1007/978-3-031-56910-4
isbn_softcover978-3-031-56909-8
isbn_ebook978-3-031-56910-4Series ISSN 2038-5714 Series E-ISSN 2532-3318
issn_series 2038-5714
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Affine Algebraic Varieties varieties. In addition, we explore the properties of these varieties and ideals by using the theory of ideals developed so far. Furthermore, we provide a proof of the Hilbert Nullstellensatz, which establishes a fundamental relation between geometry and algebra. We then apply this theorem, along wi
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Localizationring ., or, in greater generality, the construction of the field of fractions of a domain. We will define fractions using as denominators elements of a chosen subset of the ring. We will see that, when we choose the denominators in the complement of a prime ideal, this construction produces a local
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Noetherian and Artinian Rings. Primary Decomposition finitely generated and can be decomposed as a finite intersection of primary ideals. Additionally, we prove that . is Noetherian if and only if . is Noetherian, and that . is Artinian if and only if, up to isomorphism, it is a finite direct sum of local Artinian rings. This result generalizes what
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Localizationa chosen subset of the ring. We will see that, when we choose the denominators in the complement of a prime ideal, this construction produces a local ring whose maximal ideal is the extension of that prime with respect to a canonical homomorphism.
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