Book Review: Modern Higher Algebra
Hans-Berndt Brinkmann · Bulletin of the American Mathematical Society · 1938
Since the time of Dedekind it has become increasingly evident that the most satisfactory way of dealing with algebraic questions is to found the whole structure of algebra abstractly on certain fundamental abstract concepts.These are the concepts of group, ring, and field.The book we are considering here is apparently the first one in English to carry out this program.The contents of the book may be briefly summarized as follows: 1. Foundations; theory of groups, rings, fields (Chapter 1, 2). 2. Matrices and matrix algebras (Chapters 3, 4, 5, 10).3. Galois theory (Chapters 6, 7, 8, 9).4. Theory of valuation (Chapters 11, 12).