Originally published in 1984, the principal objective of this book is to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is generally regarded as one of the central and most beautiful parts of algebra and its creation marked the culmination of investigations by generations of mathematicians on one of the oldest problems in algebra, the solvability of polynomial equations by radicals.
Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the...
In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In...
This book gives a concise exposition of the theory of fields, including the Galois theory of field extensions, the Galois theory of etale algebras, and the theory of transcendental extensions. The...
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems,...
This classic in the field of abstract algebra has been called "the first systematic treatment of finite fields in the mathematical literature." Divided into two sections-"Introduction to the Galois...