Kevin McCrimmon's pre-book on alternative algebras

These are scans of Kevin McCrimmon's unfinished book on alternative algebras, as originally made available on Erhard Neher's website. This website is no longer online  (though an archived version remains accessible through the Internet Archive: https://web.archive.org/web/20260701051209/https://mysite.science.uottawa.ca/neher/Papers/alternative/ ).

I, Torben Wiedemann, have uploaded these scans to Zenodo with the kind permission of Erhard Neher in order to ensure their long-term availability.

All copyright and other intellectual property rights remain with the original author.

Below is a copy of the original text accompanying the scans on Erhard Neher's homepage:

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. 

1.1 The variety of alternative algebras
1.2 Constructions
1.3 Basic identities
1.4 Inverses
1.5 Isotopy
1.6 Quadratic ideals
1.7 Representation

2.1 Algebra 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
A.5.2 Derivations
A.5.3 Automorphisms and derivations of Cayley algebras
A.5.4 On split G_2