| 000 -LEADER |
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| fixed length control field |
a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250531b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783031569098 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.24 |
| Item number |
BAN |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Bandini, Andrea |
| 245 ## - TITLE STATEMENT |
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| Title |
Commutative Algebra through Exercises |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2024 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xi, 392 p, ; |
| Other physical details |
ill., |
| Dimensions |
24 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
64.99 |
| Price type code |
€ |
| Unit of pricing |
100.40 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
UNITEXT La Matematica per il 3+2, 2038-5757 ; |
| Volume number/sequential designation |
v.159 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| 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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Noetherian Rings |
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| Topical term or geographic name as entry element |
Commutative Algebra |
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| Topical term or geographic name as entry element |
Tensor Products |
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| Topical term or geographic name as entry element |
A-module |
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| Topical term or geographic name as entry element |
Direct sum |
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| Topical term or geographic name as entry element |
Free module |
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| Topical term or geographic name as entry element |
Gröbner basis |
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| Topical term or geographic name as entry element |
Maximal ideal |
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| Topical term or geographic name as entry element |
Monomial ordering |
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| Topical term or geographic name as entry element |
Prime ideal |
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| Topical term or geographic name as entry element |
Ring homomorphism |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Gianni, Patrizia |
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| Personal name |
Sbarra, Enrico |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |