UID:
almafu_9961989463802883
Umfang:
1 online resource (422 pages)
Ausgabe:
Third edition.
ISBN:
3-11-114252-3
Serie:
De Gruyter Textbook Series
Inhalt:
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
Anmerkung:
Frontmatter --
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Preface --
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Contents --
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1 Groups, Rings and Fields --
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2 Maximal and Prime Ideals --
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3 Prime Elements and Unique Factorization Domains --
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4 Polynomials and Polynomial Rings --
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5 Field Extensions --
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6 Field Extensions and Compass and Straightedge Constructions --
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7 Kronecker’s Theorem and Algebraic Closures --
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8 Splitting Fields and Normal Extensions --
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9 Groups, Subgroups and Examples --
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10 Normal Subgroups, Factor Groups and Direct Products --
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11 Symmetric and Alternating Groups --
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12 Solvable Groups --
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13 Group Actions and the Sylow Theorems --
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14 Free Groups and Group Presentations --
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15 Finite Galois Extensions --
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16 Separable Field Extensions --
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17 Applications of Galois Theory --
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18 The Theory of Modules --
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19 Finitely Generated Abelian Groups --
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20 Integral and Transcendental Extensions --
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21 The Hilbert Basis Theorem and the Nullstellensatz --
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22 Algebras and Group Representations --
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23 Algebraic Cryptography --
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24 Non-Commutative Group Based Cryptography --
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Bibliography --
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Index
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Issued also in print.
Weitere Ausg.:
ISBN 3-11-113951-4
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783111142524
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