| Two essential classes of rings are named after,
respectively, Emil
Artin and Emmy
Noether, artinian rings and noetherian rings, respectively.
Here are some comments about them. "Artin, with his wide interests in all fields of human endeavor, became the stimlating center of a circle of friends. His strange nickname "Ma" which he preferred to his given name Emil goes back to those days. It is short for "Mathematics"; he simply appeared to these young men as the embodiment of mathematics." (Richard Brauer) "In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians." (Albert Einstein) |
LINKS
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| Text: A First Course in Noncommutative Rings, T.Y. Lam, Graduate Texts in Mathematics, #131, Springer-Verlag 1991. | History of
Mathematics and Mathematics of many cultures |
|
| Other useful references: 1. Rings and Categories of Modules, F.W. Anderson and K.R. Fuller, Graduate Texts in Mathematics #13, 2nd Edition, Springer-Verlag, 1992. For a more advanced book by the author of our text. 2. Lectures on Modules and Rings, T.Y. Lam, Graduate Texts in Mathematics, #189, Springer-Verlag, 1999. 3. Algebra I, basic notions of algebra, A. Kostrikin and I. Shafarevich, Springer-Verlag, 1990. 4. Algebra, 2nd Edition, S. Lang, Addison-Wesley, 1984. 5. A Course in Algebra, E.B. Vinberg, Amer. Math. Soc., 2003. 7. A very nice book on commutative ring theory with an eye to algebraic geometry, see "An Introduction to Commutative Algebra", Second Edition, by M. Atiyah and I.G. Macdonald (Addison-Wesley). 8. A more advanced book (and very useful) is "Commutative Ring Theory" by H. Matsumura (Cambridge Press). 9. The following is a nice and gentle introduction to group representations: Representations and Characters of Groups, G. James and M. Liebeck, Cambridge Mathematical Textbooks, 1993. .............................................................. |
It is useful the
know the Greek alphabet (pdf): alphabet COURSE NOTES: There will be quite detailed notes on topics not taken from the text. These will be posted from time to time. The date of the current version appears on the first page of the notes. Notes |
|
| Classrooms and timetable: Tuesdays,
11:30 in KED B005 and Thursdays, 1:00 in KED B004. |
In order to read
"pdf" files you need the free software "Acrobat Reader". It is
available from acrobat web
site. |
|
| Course outline: The course will begin
some material on modules followed by much of Chapters 1, 2 and 3
of Lam. From there, the material chosen will depend on the
students
and their professors. |
||
| Assignments: There will be several. |
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| Calculation of the final mark:
To be negotiated. |
||
| Final
examination: The final exam will be a take home to be handed in
by 5:00, April 14. Question will be distributed a week in advance. |
||
| Jan. 24*: 1. Exercise
2.2 (notes) -- the exercise comes from A&F where there are almost
no misprints. It was correct as originally stated. 2. Exercise 3.1
(notes). |
| Suggested
exercises: Lam, page 25, #15, 16, 18. |
| Jan. 31*: 1. Exercise
3.4 (notes). 2. Exercise 3.6
(notes). |
| Suggested
exercises: All the exercises in the notes fall into this
category. |
| Feb. 7*: 1. Exercise
3.15 (notes). 2. Exercise
4.2 (notes) |
| Suggested
exercises: Exercises in the notes plus Lam, page 29, 2.5 and
2.7. Lam page 45, 3.1, 3.5, 3.9, 3.19. |
| Feb. 14*:
1. Exercise 4.3 (notes).
2. Exercise 4.4 (notes).
|
| Suggested
exercises: Lam, 3.23, Notes, 4.5 and 4.6. |
| Feb. 28*:
1. Exercise 4.7 (notes).
2. Exercise 4.9(i)
(notes) -- to make your lives easier, you may assume, in the last part
of the question, that the groups are finite. |
| Suggested
exercises: Exercise 4.8, 4.9 (ii); the questions in
Example 4.23. In anticipation of the next subject, Lam 4.1 and 4.2. |
| March 7*: 1. Exercise 5.3 (notes). 2. Exercise 5.5 (notes). |
| Suggested exercises: The other exercises from the notes, Section 5. Most of the exercises in ¶ 5 of Lam are accessible. |
| March 14*: 1. Exercise 6.1 (notes). 2. Exercise 6.2 (notes). |
| Suggested
exercises: Notes, 6.3(new), 6.4, 6.5 and 6.6. |
| March
21*: 1. Exercise 6.7
(notes). 2. Exercise 6.8
(notes) **See "Final exam" above. |
| Suggested
exercises: Lam:19.1, 2, 3, 5, 6, 14. |
| March
28*: 1. Exercise 6.9
(notes). 2. Exercise
6.12 (notes) |
| Suggested
exercises: Other exercises from the notes and Exercises 21.11 -
15 in the text. |
| April
4*: 1. Exercise 6.15
(notes). 2. Exercise
6.16 (notes). |
| Suggested
exercises: Exercises 6.13 and 6.14 (notes), Lam: exercises
21.18 and 21.21. |
| Take home final exam QUESTIONS. If there are any
ambiguities, do not hesitate to ask me for clarification. |