The Theory of Rings

Description

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