Math 120a
Abstract Algebra
Fall 2014-15
MWF 9:00 am // 257 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Math Courses

Instructor: Dinakar Ramakrishnan, 278 Sloan, 626-395-4348,
Office Hours: Fri: 4:00 - 5:00 PM
Grader: Serin Hong, 382 Sloan, 395-4081,
Office Hours: Sun: 3:00 - 4:00 PM


The take home Final Exam may be picked from the Math office in Sloan after 2PM on Monday, the 1st of December. It is a timed (4 hr) exam and is due by noon on Wednesday, the 10th of december.

1. The first Homework Assignment will be posted on Tuesday, Sep. 30, 2014. It will be due next Monday (October 6, 2014) by 9AM; please leave the homework solutions in the slot marked Ma120a in the second floor of Sloan outside the math office (Sloan 253).
2. There will be no midterm exam, just HW and a comprehensive final exam, the former worth 60% of the grade, and the latter worth the rest.

Course Description

The first term of Math 120 will be devoted principally to Commutative Algebra, including categories and functors, basic module theory, products and coproducts, exact sequences, free modules, tensor products, flat modules, localization, chain conditions, projective and injective modules, and some homological algebra. The material in a substantial undergraduate algebra course (such as our own Math 5) will be assumed.

Topics in more detail:

1.  Basics properties of rings (not necessarily commutative, but always with 1), modules and algebras, and their homomorphisms; rings of endomorphisms;  examples.

2.  Categories and functors

3.  Tensor products

4.  Flat, free, projective and injective modules

5.  Noetherian property, Hilbert basis theorem

6.  Algebraic sets, Integral extensions, Nullstellensatz

7.  Primary decompositions, Associated primes

8.  Transcendental extensions, Differentials and derivations

9.  Localization, Spectrum of a ring

10. Completions, dimension

11. Discrete valuation rings

12. Homology



Grading: Homework = 60% , Final = 40% .

Homework: You can work together but must write up your own solution in your own words, rather than copy a classmate’s solution. Except in unusual circumstances, homework will not be accepted more than a week late and at most one late homework set will be accepted.  You should see the instructor in advance if it is necessary to turn in homework late.


  • Algebra by Serge Lang, Springer, ISBN: 0387905189

For further reading, see

  • Commutative Ring Theory by H. Matsumura, ISBN-13: 978-0521367646

Lecture Notes

Date Description


Date Description


Due Date Homework  Solutions
October 6, 2014,  9AM
October 13, 2014, 9AM
October 20, 2014
October 28, 2014
November 3, 2014
November 10, 2014
November 17, 2014
November 24, 2014

  | © California Institute of Technology | Questions?  scroomes @