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