The Theory of Rings

Title page
Chapter 1 Examples and Fundamental Properties of Rings
1. Definitions and Simple Properties
2. Imbedding in a Ring with Unity
3. Algebras
4. Formal Power Series
5. Direct Sums
Chapter 2 Ideals and Homomorphisms
6. Ideals
7. Sums and Direct Sums of Ideals
8. Ideal Products and Nilpotent Ideals
9. Some Condictions on Ideals
10. Ideals in Complete Matrix Rings
11. Residue-Class Rings
12. Homomorphisms
Chpater 3 Subdirect Sums of Rings
13. Definitions and Fundamental Properties
14. Zorn's Lemma
15. Subdirectly Irreducible Rings
16. Boolean Rings
17. A Special Result
Chapter 4 Prime Ideals and the Prime Radical
18. Prime Ideals and m-Systems
19. Semi-Prime Ideals
20. The Prime Radical of Ring
21. Prime Rings
22. The Descending Chain Condition and the Prime Radical
Chapter 5 Endomorphisms and Linear Transformations
23. Rings of Endomorphisms
24. Irreducible Rings of Endomorphisms
25. R-Modules and Rings of Endomorphisms
26. Irreducible Rings and Vector Spaces
27. Dense Rings of Linear Transformations
28. Subspaces and the Descending Chain Condition
29. Some Properties of a Ring D_n
30. The Wedderburn-Artin Theorem
Chapter 6 The Jacobson Radical
31. Preliminary Concepts
32. Definition and Simple Properties
33. Further Properties of the Jacobson Radical
34. The Descending Chain Condition
Chapter 7 Some Additional Topics
35. Idempotents and Regular Elements of Dense Rings
36. Some Further Results on Dense Rings
37. Another Radical of a Ring
Notes
References
Index