東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

A textbook of algebraic number theory

Khanduja, Sudesh Kaur.

FindBook

Google Book

Amazon

博客來

A textbook of algebraic number theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A textbook of algebraic number theory/ by Sudesh Kaur Khanduja.
作者:	Khanduja, Sudesh Kaur.
出版者:	Singapore :Springer Nature Singapore : : 2022.,
面頁冊數:	xviii, 253 p. :ill., digital ;24 cm.
內容註:	1. Algebraic Integers, Norm and Trace -- 2. Integral Basis and Discriminant -- 3. Properties of the Ring of Algebraic Integers -- 4. Splitting of Rational Primes and Dedekind's Theorem -- 5. Dirichlet's Unit Theorem -- 6. Prime Ideal Decomposition in Relative Extensions -- 7. Relative Discriminant and Dedekind's Theorem on Ramified -- 8. Ideal Class Group -- 9. Dirichlet's Class Number Formula and its Applications -- 10. Simplified Class Number Formula for Cyclotomic, Quadratic Fields.
Contained By:	Springer Nature eBook
標題:	Algebraic number theory. -
電子資源:	https://doi.org/10.1007/978-981-16-9150-8
ISBN:	9789811691508

A textbook of algebraic number theory
Khanduja, Sudesh Kaur.

A textbook of algebraic number theory[electronic resource] /by Sudesh Kaur Khanduja. - Singapore :Springer Nature Singapore :2022. - xviii, 253 p. :ill., digital ;24 cm. - UNITEXT. La matematica per il 3+2,v. 1352038-5757 ;. - UNITEXT.La matematica per il 3+2 ;v. 135..

1. Algebraic Integers, Norm and Trace -- 2. Integral Basis and Discriminant -- 3. Properties of the Ring of Algebraic Integers -- 4. Splitting of Rational Primes and Dedekind's Theorem -- 5. Dirichlet's Unit Theorem -- 6. Prime Ideal Decomposition in Relative Extensions -- 7. Relative Discriminant and Dedekind's Theorem on Ramified -- 8. Ideal Class Group -- 9. Dirichlet's Class Number Formula and its Applications -- 10. Simplified Class Number Formula for Cyclotomic, Quadratic Fields.

This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number theory including Dedekind's theorem on splitting of primes, Dirichlet's unit theorem, Minkowski's convex body theorem, Dedekind's discriminant theorem, Hermite's theorem on discriminant, Dirichlet's class number formula, and Dirichlet's theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned together with the progress made in the direction of each problem. Following the classical approach of Dedekind's theory of ideals, the book aims at arousing the reader's interest in the current research being held in the subject area. It not only proves basic results but pairs them with recent developments, making the book relevant and thought-provoking. Historical notes are given at various places. Featured with numerous related exercises and examples, this book is of significant value to students and researchers associated with the field. The book also is suitable for independent study. The only prerequisite is basic knowledge of abstract algebra and elementary number theory.

ISBN: 9789811691508

Standard No.: 10.1007/978-981-16-9150-8doiSubjects--Topical Terms:

532574
Algebraic number theory.

LC Class. No.: QA247 / .K43 2022

Dewey Class. No.: 512.74

A textbook of algebraic number theory
LDR:02808nmm a2200337 a 4500 001 2300689
003 DE-He213
005 20220426065106.0
006 m d
007 cr nn 008maaau
008 230324s2022 si s 0 eng d
020 $a 9789811691508 $q (electronic bk.)
020 $a 9789811691492 $q (paper)
024 7 $a 10.1007/978-981-16-9150-8 $2 doi
035 $a 978-981-16-9150-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA247 $b .K43 2022
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.74 $2 23
090 $a QA247 $b .K45 2022
100 1 $a Khanduja, Sudesh Kaur. $3 3599438
245 1 2 $a A textbook of algebraic number theory $h [electronic resource] / $c by Sudesh Kaur Khanduja.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2022.
300 $a xviii, 253 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT. La matematica per il 3+2, $x 2038-5757 ; $v v. 135
505 0 $a 1. Algebraic Integers, Norm and Trace -- 2. Integral Basis and Discriminant -- 3. Properties of the Ring of Algebraic Integers -- 4. Splitting of Rational Primes and Dedekind's Theorem -- 5. Dirichlet's Unit Theorem -- 6. Prime Ideal Decomposition in Relative Extensions -- 7. Relative Discriminant and Dedekind's Theorem on Ramified -- 8. Ideal Class Group -- 9. Dirichlet's Class Number Formula and its Applications -- 10. Simplified Class Number Formula for Cyclotomic, Quadratic Fields.
520 $a This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number theory including Dedekind's theorem on splitting of primes, Dirichlet's unit theorem, Minkowski's convex body theorem, Dedekind's discriminant theorem, Hermite's theorem on discriminant, Dirichlet's class number formula, and Dirichlet's theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned together with the progress made in the direction of each problem. Following the classical approach of Dedekind's theory of ideals, the book aims at arousing the reader's interest in the current research being held in the subject area. It not only proves basic results but pairs them with recent developments, making the book relevant and thought-provoking. Historical notes are given at various places. Featured with numerous related exercises and examples, this book is of significant value to students and researchers associated with the field. The book also is suitable for independent study. The only prerequisite is basic knowledge of abstract algebra and elementary number theory.
650 0 $a Algebraic number theory. $3 532574
650 1 4 $a Number Theory. $3 891078
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a UNITEXT. $p La matematica per il 3+2 ; $v v. 135. $3 3599439
856 4 0 $u https://doi.org/10.1007/978-981-16-9150-8
950 $a Mathematics and Statistics (SpringerNature-11649)