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Modern Algebra: Lecture Notes

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Author(s): Prof. James McKernan
Publisher: Massachusetts Institute of Technology (MIT)
Year: 2013

Language: English
City: Cambridge, MA
Tags: 18.703; abstract algebra; maths; math; mathematics

1. Groups
2. Subgroups
3. Cosets
4. Cyclic groups
5. Permutation groups
6. Conjugation in Sn
7. Isomorphisms
8. Homomorphisms and kernels
9. Quotient Groups
10. The isomorphism theorems
11. The Alternating Groups
12. Presentations and Groups of small order
13. Sylow Theorems and applications
14. Rings
15. Basic Properties of Rings
16. Ring Homomorphisms and Ideals
17. Field of fractions
18. Prime and Maximal Ideals
19. Special Domains
20. Euclidean Domains
21. Polynomial rings
22. A quick primality test
23. Group actions and automorphisms