Pre-Book on Alternative Algebras

Dear visitor: Below are scans of sections of Kevin McCrimmon's unfinished book on alternative algebras, written in the late 1970's and early 1980's. They are posted here with his kind permission.

The scans were done from a loose collection of xerox copies, all belonging to my colleague Michel Racine (as you can easily see). I have tried to follow the section numbering as much as I could figure it out. It may not always be the one intended by the author. Some sections appear twice, for those interested in the history of mathematics. There are 78 files, approximately 63 MB.

With all my apologies for the bad quality of the scans,

Erhard Neher.

Here are the links to the individual files:

2.1 Algebras of degree 2
2.2 Composition algebras
2.3 Cayley-Dickson process
2.4 Classification of composition algebras
2.5 Triality
2.5.2 Triality and local triality
2.6 Quadratic ideals
2.6.2 Inner ideals
2.7 Bimodules
2.7.2 Bimodules II
2.8 Bimodules with involution
2.8.2 Bimodules with involution II
2.9 Derivations

3.1 Nucleus, center and centroid
3.2 Basic associativity tests
3.3 Associativity Theorems
3.4 Associativity from commutativity

4.1 Nilpotence
4.2 Solvability
4.3 Semiprimeness
4.4 Local nilpotence
4.5 Strong primeness
4.6 Nilness
4.7 Quasi-Invertibility
4.8 Radicals of related algebras
4.9 Coincidence of radicals

5.1 Products of ideals
5.2 One-sided ideals
5.3 Products of one-sided ideals
5.4 Jordan ideals
5.5 Quadratic ideals

6.1 The nature of idempotents
6.2 Peirce decompositions
6.3 Peirce relations
6.4 Ideal-building
6.5 Connectivity
6.6 Cayley Matrix Units
6.7 Lifting Theorems

7.1 Degree 2 algebras
7.2 Composition algebras
7.3 The Cayley-Dickson process
7.4 Classification of composition algebras

8.1 The first Structure Theorem
8.2 The second structure theorem
8.3 Structure of bimodules
8.4 Structure of derivations
8.5 Splitting theorems
8.6 Malcev's theorem

9.1 Alternative division algebras
9.1.2 Alternative division algebras (previous version)
9.2 Simple alternative algebras
9.3 Prime algebras
9.4 Slater's approach to the structure theory
9.4.2 Slater's approach to the structure theory (previous version)
9.5 Central and nuclear involutions
9.6 The Herstein-Kleinfeld-Osborn Theorem

A.1.1 Projective planes
A.1.2 Affine planes
A.1.3 From projective to affine and back again
A.1.4 Planes from rings

A.2.1 The variety of left Moufang algebras
A.2.2 Units, inverses, and homotopes
A.2.3 Division rings
A.2.4 Bruck's example
A.2.5 Degree 2 algebras (again)

A.3 General Structure Theory
A.4 Left alternative algebras

A.5.1 Automorphisms I
A.5.2 Automorphisms II (Derivations)
A.5.3 Automorphisms III
A.5.4 Automorphisms IV