Abstract Algebra : : Applications to Galois Theory, Algebraic Geometry and Cryptography / / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen.
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theore...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2011] ©2011 |
Year of Publication: | 2011 |
Language: | English |
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Carstensen, Celine, author. aut http://id.loc.gov/vocabulary/relators/aut Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen. Berlin ; Boston : De Gruyter, [2011] ©2011 1 online resource (366 p.) : Num. figs. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1 Groups, Rings and Fields -- 2 Maximal and Prime Ideals -- 3 Prime Elements and Unique Factorization Domains -- 4 Polynomials and Polynomial Rings -- 5 Field Extensions -- 6 Field Extensions and Compass and Straightedge Constructions -- 7 Kronecker’s Theorem and Algebraic Closures -- 8 Splitting Fields and Normal Extensions -- 9 Groups, Subgroups and Examples -- 10 Normal Subgroups, Factor Groups and Direct Products -- 11 Symmetric and Alternating Groups -- 12 Solvable Groups -- 13 Groups Actions and the Sylow Theorems -- 14 Free Groups and Group Presentations -- 15 Finite Galois Extensions -- 16 Separable Field Extensions -- 17 Applications of Galois Theory -- 18 The Theory of Modules -- 19 Finitely Generated Abelian Groups -- 20 Integral and Transcendental Extensions -- 21 The Hilbert Basis Theorem and the Nullstellensatz -- 22 Algebraic Cryptography -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Nov 2021) Algebra, Abstract. Cryptography. Galois theory. Geometry, Algebraic. Universelle Algebra. MATHEMATICS / Algebra / Abstract. bisacsh Algebra. Algebraic Structure. Cryptology. Fine, Benjamin, author. aut http://id.loc.gov/vocabulary/relators/aut Rosenberger, Gerhard, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011 9783110261189 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011 9783110261233 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011 9783110261202 ZDB-23-DMN https://doi.org/10.1515/9783110250091 https://www.degruyter.com/isbn/9783110250091 Cover https://www.degruyter.com/document/cover/isbn/9783110250091/original |
language |
English |
format |
eBook |
author |
Carstensen, Celine, Carstensen, Celine, Fine, Benjamin, Rosenberger, Gerhard, |
spellingShingle |
Carstensen, Celine, Carstensen, Celine, Fine, Benjamin, Rosenberger, Gerhard, Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1 Groups, Rings and Fields -- 2 Maximal and Prime Ideals -- 3 Prime Elements and Unique Factorization Domains -- 4 Polynomials and Polynomial Rings -- 5 Field Extensions -- 6 Field Extensions and Compass and Straightedge Constructions -- 7 Kronecker’s Theorem and Algebraic Closures -- 8 Splitting Fields and Normal Extensions -- 9 Groups, Subgroups and Examples -- 10 Normal Subgroups, Factor Groups and Direct Products -- 11 Symmetric and Alternating Groups -- 12 Solvable Groups -- 13 Groups Actions and the Sylow Theorems -- 14 Free Groups and Group Presentations -- 15 Finite Galois Extensions -- 16 Separable Field Extensions -- 17 Applications of Galois Theory -- 18 The Theory of Modules -- 19 Finitely Generated Abelian Groups -- 20 Integral and Transcendental Extensions -- 21 The Hilbert Basis Theorem and the Nullstellensatz -- 22 Algebraic Cryptography -- Bibliography -- Index |
author_facet |
Carstensen, Celine, Carstensen, Celine, Fine, Benjamin, Rosenberger, Gerhard, Fine, Benjamin, Fine, Benjamin, Rosenberger, Gerhard, Rosenberger, Gerhard, |
author_variant |
c c cc c c cc b f bf g r gr |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Fine, Benjamin, Fine, Benjamin, Rosenberger, Gerhard, Rosenberger, Gerhard, |
author2_variant |
b f bf g r gr |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Carstensen, Celine, |
title |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / |
title_sub |
Applications to Galois Theory, Algebraic Geometry and Cryptography / |
title_full |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen. |
title_fullStr |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen. |
title_full_unstemmed |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen. |
title_auth |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / |
title_alt |
Frontmatter -- Preface -- Contents -- 1 Groups, Rings and Fields -- 2 Maximal and Prime Ideals -- 3 Prime Elements and Unique Factorization Domains -- 4 Polynomials and Polynomial Rings -- 5 Field Extensions -- 6 Field Extensions and Compass and Straightedge Constructions -- 7 Kronecker’s Theorem and Algebraic Closures -- 8 Splitting Fields and Normal Extensions -- 9 Groups, Subgroups and Examples -- 10 Normal Subgroups, Factor Groups and Direct Products -- 11 Symmetric and Alternating Groups -- 12 Solvable Groups -- 13 Groups Actions and the Sylow Theorems -- 14 Free Groups and Group Presentations -- 15 Finite Galois Extensions -- 16 Separable Field Extensions -- 17 Applications of Galois Theory -- 18 The Theory of Modules -- 19 Finitely Generated Abelian Groups -- 20 Integral and Transcendental Extensions -- 21 The Hilbert Basis Theorem and the Nullstellensatz -- 22 Algebraic Cryptography -- Bibliography -- Index |
title_new |
Abstract Algebra : |
title_sort |
abstract algebra : applications to galois theory, algebraic geometry and cryptography / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2011 |
physical |
1 online resource (366 p.) : Num. figs. |
contents |
Frontmatter -- Preface -- Contents -- 1 Groups, Rings and Fields -- 2 Maximal and Prime Ideals -- 3 Prime Elements and Unique Factorization Domains -- 4 Polynomials and Polynomial Rings -- 5 Field Extensions -- 6 Field Extensions and Compass and Straightedge Constructions -- 7 Kronecker’s Theorem and Algebraic Closures -- 8 Splitting Fields and Normal Extensions -- 9 Groups, Subgroups and Examples -- 10 Normal Subgroups, Factor Groups and Direct Products -- 11 Symmetric and Alternating Groups -- 12 Solvable Groups -- 13 Groups Actions and the Sylow Theorems -- 14 Free Groups and Group Presentations -- 15 Finite Galois Extensions -- 16 Separable Field Extensions -- 17 Applications of Galois Theory -- 18 The Theory of Modules -- 19 Finitely Generated Abelian Groups -- 20 Integral and Transcendental Extensions -- 21 The Hilbert Basis Theorem and the Nullstellensatz -- 22 Algebraic Cryptography -- Bibliography -- Index |
isbn |
9783110250091 9783110238570 9783110238471 9783110637205 9783110261189 9783110261233 9783110261202 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA162 |
callnumber-sort |
QA 3162 C375 42011 |
url |
https://doi.org/10.1515/9783110250091 https://www.degruyter.com/isbn/9783110250091 https://www.degruyter.com/document/cover/isbn/9783110250091/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110250091 |
oclc_num |
979753468 |
work_keys_str_mv |
AT carstensenceline abstractalgebraapplicationstogaloistheoryalgebraicgeometryandcryptography AT finebenjamin abstractalgebraapplicationstogaloistheoryalgebraicgeometryandcryptography AT rosenbergergerhard abstractalgebraapplicationstogaloistheoryalgebraicgeometryandcryptography |
status_str |
n |
ids_txt_mv |
(DE-B1597)122849 (OCoLC)979753468 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011 |
is_hierarchy_title |
Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography / |
container_title |
Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 |
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