Abstract Algebra

Course Description
The second term of Math 120 will be devoted primarily to .Field and Galois Theory. Time permitting, topics should include: 

Field extensions: Algebraic closure. Splitting fields and normal extensions. Separable and Inseparable extensions and degree. Primitive element theorem. Linear independence of characters. Traces and norms. Normal basis theorem. 

Galois theory: Galois extensions. Absolute Galois group. Galois theory for infinite extensions.

Examples: Finite fields. Cyclotomic fields.

Galois Cohomology: Galois Cohomology. Hilbert's 90 theorem.

Kummer Theory: Cyclic extensions. Solvable extensions. Kummer Theory.

Transcendental Extensions: Transcendental extensions. Transcendence bases theorem. 

Ring extensions: Integral extensions. Noether Normalization Theorem. Integral closure. Integral Galois extensions. Going-up theorem. Decomposition groups. Extension of homomorphisms. Valuation rings.

Complements: Introduction to local fields. Dedekind domains. DVR's.


Course Meeting Time and Location
Monday, Wednesday and Friday
9:00 - 9:55 am
104 Math Building (Building 15)

Course Instructor Contact Information and Office Hours
205 Math Building (Building 15)

TA Contact Information and Office Hours


Textbook
Algebra, Serge Lang, Springer, ISBN: 978-0-387-95385-4



Course Policies and Grading Breakdown
There will be no midterms nor final exam. The grade will be based on homework. Homework will be posted here every Wednesday and will be due the following Wednesday at 4pm. Homework must be typed in Tex and can be handed in either in hard copy or in electronic version. Late homework will not be accepted EXCEPT ONE time (per term). You may email me PRIOR to the due time requesting an extension of up to one week (for the last HW up to two days) and it will granted.

Assignments
 Date Posted Assignment  Due Date 
 1/03/2018 PS1.pdf 1/10/2018 4pm 
 1/10/2018 PS2.pdf  1/17/2018 4pm
 1/17/2018 PS3.pdf  1/24/2018 4pm 
 1/24/2018   1/31/2018 4pm
 1/31/2018   2/07/2018 4pm 
 2/07/2018   2/14/2018 4pm 
 2/14/2018   2/21/2018 4pm 
 2/21/2018   2/28/2018 4pm
 2/28/2018   3/07/2018 4pm
 3/07/2018    3/14/2018 4pm

Ċ
PS1.pdf
(34k)
Xinwen Zhu,
Jan 3, 2018, 4:35 PM
Ċ
PS2.pdf
(34k)
Xinwen Zhu,
Jan 10, 2018, 9:06 PM
Ċ
PS3.pdf
(68k)
Xinwen Zhu,
Jan 17, 2018, 10:33 PM