國立高雄大學圖資館 |

Language: English

Back

Commutative algebra through exercises

Record Type:	Electronic resources : Monograph/item
Title/Author:	Commutative algebra through exercisesby Andrea Bandini, Patrizia Gianni, Enrico Sbarra.
Author:	Bandini, Andrea.
other author:	Gianni, P.
Published:	Cham :Springer International Publishing :2024.
Description:	xi, 392 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Commutative algebra.
Online resource:	https://doi.org/10.1007/978-3-031-56910-4
ISBN:	9783031569104$q(electronic bk.)

Commutative algebra through exercises
Bandini, Andrea.

Commutative algebra through exercises[electronic resource] /by Andrea Bandini, Patrizia Gianni, Enrico Sbarra. - Cham :Springer International Publishing :2024. - xi, 392 p. :ill., digital ;24 cm. - UNITEXT. La matematica per il 3+2,1592038-5757 ;. - UNITEXT.La matematica per il 3+2 ;v. 136..

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.

ISBN: 9783031569104$q(electronic bk.)

Standard No.: 10.1007/978-3-031-56910-4doiSubjects--Topical Terms:

190842
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Commutative algebra through exercises
LDR:03099nmm a2200337 a 4500 001 667193
003 DE-He213
005 20240712125359.0
006 m d
007 cr nn 008maaau
008 250107s2024 sz s 0 eng d
020 $a 9783031569104$q(electronic bk.)
020 $a 9783031569098$q(paper)
024 7 $a 10.1007/978-3-031-56910-4 $2 doi
035 $a 978-3-031-56910-4
040 $a GP $c GP
041 1 $a eng $h ita
050 4 $a QA251.3
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.44 $2 23
090 $a QA251.3 $b .B214 2024
100 1 $a Bandini, Andrea. $3 979999
240 1 0 $a Esercizi di algebra commutativa. $l English
245 1 0 $a Commutative algebra through exercises $h [electronic resource] / $c by Andrea Bandini, Patrizia Gianni, Enrico Sbarra.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a xi, 392 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT. La matematica per il 3+2, $x 2038-5757 ; $v 159
520 $a 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 $a Commutative algebra. $3 190842
650 1 4 $a Algebra. $3 188312
700 1 $a Gianni, P. $3 980000
700 1 $a Sbarra, Enrico. $3 980001
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a UNITEXT. $p La matematica per il 3+2 ; $v v. 136. $3 922584
856 4 0 $u https://doi.org/10.1007/978-3-031-56910-4
950 $a Mathematics and Statistics (SpringerNature-11649)