A Taste of Jordan Algebras Book

	Preface
	Standard Notation
	A Colloquial Survey of Jordan Theory	1
Pt. I	A Historical Survey of Jordan Structure Theory
1	Jordan Algebras in Physical Antiquity	39
2	Jordan Algebras in the Algebraic Renaissance	51
3	Jordan Algebras in the Enlightenment	69
4	The Classical Theory	81
5	The Final Classical Formulation	95
6	The Classical Methods	99
7	The Russian Revolution	107
8	Zel'manov's Exceptional Methods	114
Pt. II	The Classical Theory
1	The Category of Jordan Algebras	132
2	The Category of Alternative Algebras	153
3	Three Special Examples	168
4	Jordan Algebras of Cubic Forms	186
5	Two Basic Principles	199
6	Inverses	211
7	Isotopes	220
8	Peirce Decomposition	235
9	Off-Diagonal Rules	247
10	Peirce Consequences	253
11	Spin Coordinatization	259
12	Hermitian Coordinatization	268
13	Multiple Peirce Decompositions	278
14	Multiple Peirce Consequences	292
15	Hermitian Symmetries	301
16	The Coordinate Algebra	308
17	Jacobson Coordinatization	312
18	Von Neumann Regularity	318
19	Inner Simplicity	325
20	Capacity	330
21	Herstein - Kleinfeld - Osborn Theorem	335
22	Osborn's Capacity 2 Theorem	348
23	Classical Classification	356
Pt. III	Zel'manov's Exceptional Theorem
1	The Radical	362
2	Begetting and Bounding Idempotents	381
3	Bounded Spectra Beget Capacity	388
4	Absorbers of Inner Ideals	397
5	Primitivity	410
6	The Primitive Heart	422
7	Filters and Ultrafilters	427
8	Ultraproducts	433
9	The Final Argument	440
Pt. IV	Appendices
A	Cohn's Special Theorems	447
B	Macdonald's Theorem	455
C	Jordan Algebras of Degree 3	476
D	The Jacobson-Bourbaki Density Theorem	501
E	Hints	506
Pt. V	Indexes
A	Index of Collateral Readings	524
B	Pronouncing Index of Names	531
	C: Index of Notations	536
	D: Index of Statements	545
	E: Index of Definitions	555