Proofs of the Theorems

  • Juliusz Brzeziński
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


This chapter contains the proofs to all theorems presented in the book. Only a few theorems, which are typically covered in an introductory course on groups, rings and fields are proved in the Appendix. A proof of the fundamental theorem of algebra is given in connection with the exercises in Chap. 13.


  1. [BR]
    T.R. Berger, I. Reiner, A proof of the normal basis theorem, Am. Math. Monthly, 82 (1975), 915–918.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [L]
    S. Lang, Algebra, Third Edition, Addison-Wesley, 1993.zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Juliusz Brzeziński
    • 1
    • 2
  1. 1.Department of Mathematical SciencesUniversity of GothenburgGöteborgSweden
  2. 2.Chalmers University of TechnologyGöteborgSweden

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