Finite Fields and Galois Rings

A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.Contents: Sets and Integers Groups Fields and Rings Polynomials Residue Class Rings Structure of Finite Fields Further Properties of Finite Fields Bases Factoring Polynomials over Finite Fields Irreducible Polynomials over Finite Fields Quadratic Forms over Finite Fields More Group Theory and Ring Theory Hensel's Lemma and Hensel Lift Galois Rings Readership: Upper level undergraduates, graduate students and lecturers in algebra. Keywords: Finite Fields; Galois Rings; Ring; Field