Rings and Fields

Abstract

Although my assumption in writing this book is that my readers have some knowledge of abstract algebra, a few reminders of basic definitions may be necessary, and have the added advantage of establishing the notations and conventions I shall use throughout the book. Introductory texts in abstract algebra (see [13], for example) are often titled or subtitled “Groups, Rings and Fields”, with fields playing only a minor part. Yet the theory of fields, through which both geometry and the classical theory of equations are illuminated by abstract algebra, contains some of the deepest and most remarkable insights in all mathematics. The hero of the narrative ahead is Evariste Galois,¹ who died in a duel before his twenty-first birthday.

Evariste Galois, 1811–1832.