Commutative Algebra through Exercises (Record no. 61517)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04436nam a22005055i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-56910-4 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112624.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240712s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031569104 |
| -- | 978-3-031-56910-4 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-56910-4 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA150-272 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Bandini, Andrea. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 80389 |
| 245 10 - TITLE STATEMENT | |
| Title | Commutative Algebra through Exercises |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Andrea Bandini, Patrizia Gianni, Enrico Sbarra. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XI, 392 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | La Matematica per il 3+2, |
| International Standard Serial Number | 2038-5757 ; |
| Volume/sequential designation | 159 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Part I Theory -- 1 Rings -- 2 The Ring K[x1, . . . , xn] -- 3 Affine Algebraic Varieties -- 4 Modules -- 5 Tensor Product -- 6 Localization -- 7 Noetherian and Artinian Rings. Primary Decomposition -- Part II Exercises -- 8 Rings and Ideals -- 9 Polynomials, Gröbner Bases, Resultant, and Varieties -- 10 Modules -- 11 Tensor Product -- 12 Localization -- 13 Noetherian and Artinian Modules -- 14 True or False? -- 15 Review Exercises -- Part III Proofs and Solutions -- 16 Proofs of Theoretical Results -- 17 Solutions to the Exercises. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 1501 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 1501 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Gianni, Patrizia. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 80390 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Sbarra, Enrico. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 80391 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031569098 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031569111 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | La Matematica per il 3+2, |
| International Standard Serial Number | 2038-5757 ; |
| Volume number/sequential designation | 159 |
| 9 (RLIN) | 70145 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-56910-4">https://doi.org/10.1007/978-3-031-56910-4</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-SXMS |
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