Abstract Algebra
eBook - PDF

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

  1. 421 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

About this book

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 and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.

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Yes, you can access Abstract Algebra by Celine Carstensen-Opitz,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2019
eBook ISBN
9783110603996
Edition
2

Table of contents

  1. Preface
  2. Preface to the second edition
  3. Contents
  4. 1. Groups, rings and fields
  5. 2. Maximal and prime ideals
  6. 3. Prime elements and unique factorization domains
  7. 4. Polynomials and polynomial rings
  8. 5. Field extensions
  9. 6. Field extensions and compass and straightedge constructions
  10. 7. Kronecker’s theorem and algebraic closures
  11. 8. Splitting fields and normal extensions
  12. 9. Groups, subgroups, and examples
  13. 10. Normal subgroups, factor groups, and direct products
  14. 11. Symmetric and alternating groups
  15. 12. Solvable groups
  16. 13. Groups actions and the Sylow theorems
  17. 14. Free groups and group presentations
  18. 15. Finite Galois extensions
  19. 16. Separable field extensions
  20. 17. Applications of Galois theory
  21. 18. The theory of modules
  22. 19. Finitely generated Abelian groups
  23. 20. Integral and transcendental extensions
  24. 21. The Hilbert basis theorem and the nullstellensatz
  25. 22. Algebras and group representations
  26. 23. Algebraic cryptography
  27. Bibliography
  28. Index