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LECTURES ON FINITE FIELDS AND GALOIS RINGS
by Zhe-Xian Wan (Chinese Academy of Sciences, China)
About the Author
Born in Shandong, China, in 1927, Zhe-Xian Wan graduated from Tsinghua University, Beijing, in 1948 and became a teacher at the same university. In 1950 he joined the Chinese Academy of Sciences, and in 1978 he was appointed Research Professor at the Academy. He is also a member of the Chinese Academy of Sciences.
Professor Wan's main research interests are algebra (pure and applied), combinatorics and coding theory. In addition to nearly 130 papers, he has published 18 books in these areas, including Classical Groups (jointly with L K Hua), Lie Algebras, Algebra and Coding, Introduction to Kac-Moody Algebras, Geometry of Classical Groups over Finite Fields, Geometry of Matrices and Quaternary Codes.
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Contents:
- Sets and Integers
- Groups
- Fields and Rings
- Polynomials
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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.
"This is a thorough treatment of the theory of finite fields and Galois rings, the bulk of the text being devoted to the former ... The book is well written."
| 352pp |
Pub. date: Aug 2003 |
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