Book Review: Introduction to the theory of abstract algebras
Paul M. Cohn · Bulletin of the American Mathematical Society · 1969
product in older books, are supposed to be known.For this, as well as for some of the details left out, the reader might find useful the book Structure of rings by N. Jacobson, which is a standard reference, but it is also more general and more difficult to read.There are several misprints in the book such as exponents which appear as factors, some changed symbols, a couple of exponents omitted, etc.We think that only two of the misprints have some importance.One which could cause some trouble when only the theorem is consulted appears in the statement of Theorem 5.1.7where instead of ^t-\Xi(p)XiQ>) ~^f it should read ]C?=iX*(#)Xt(fr) =0.In Theorem 6.3.2 the ring B is a direct product (or complete direct sum) of fields, and not just a direct sum as stated.This book will appeal to many a reader.It would be wonderful as a textbook, and, in fact, it is based on the author's lecture notes published by the University of Chicago.But it can also be useful as a reference and as a source of information on counterexamples and recent literature.Only people looking for the most general form of a particular theorem are advised to turn to other books, but the reader interested in studying or reviewing its subject-matter or looking for a rounded account of it could do no better than choosing this book for this purpose.