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Title: Hypercomplex Numbers: An Elementary Introduction to Algebras by A.S. Solodovnikov, A. Shenitzer, I. L. Kantor ISBN: 0-387-96980-2 Publisher: Springer Verlag Pub. Date: June, 1989 Format: Hardcover Volumes: 1 List Price(USD): $74.95

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Average Customer Rating: 4 (1 review)

Rating: 4
Summary: This is Written Too Well!
Comment: To begin with, I think this text is overpriced. It is a shame that it is overpriced because that is the only reason I gave it less than five stars. I believe it to be too expensive because it is a relatively quick read.

Now if you are not familiar with generalizations of complex numbers such as the quaternions and the cayley numbers, this is an excellent introduction to them. By the end of the book you will understand why, depending on how you define the word 'interesting', the only 'interesting' algebras are those of the reals, complex, quaternions, and cayleys (up to isomorphism). The proofs of Frobenius' and Hurwitz's Thms. are wonderful.

One thing I must say about this book is that it is truly amazing how there is no prerequisite besides our familiar algebra! This book is great for undergraduates and would be a nice supplement for someone taking a first abstract algebra course. Again, I cannot believe how readable the book is. An advanced reader could probably blow through this book in a few days, but again it does prove the theorems of Hurwitz and Frobenius with such clarity that an advanced reader not familiar with these wonderful theorems would certainly enjoy the later parts of this book.