Dirk Hachenberger Book order

The book offers a comprehensive exploration of finite fields, emphasizing their foundational aspects and algebraic closures. It introduces advanced topics rarely covered in textbooks, such as the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for polynomial factorization over finite fields. This self-contained monograph is designed for readers seeking a deeper understanding of these complex mathematical concepts.

The book delves into the significance of finite fields in both pure and applied mathematics, highlighting their roles in areas like coding theory and cryptography. It focuses on the Normal Basis Theorem, a pivotal result in field theory that ensures the existence of a basis for finite dimensional Galois extensions. The historical context includes K. Hensel's 1888 proof, while recent advancements emphasize the practical applications of normal bases in computational arithmetic, making their construction a key research area in finite field theory.