Math 120a  
Abstract Algebra  
Fall 201415  
MWF 9:00 am
// 257 Sloan


Instructor:
Dinakar Ramakrishnan, 278
Sloan, 6263954348, dinakar@caltech.edu
Office Hours: Fri: 4:00  5:00 PM Grader: Serin Hong, 382 Sloan, 3954081, shong2@caltech.edu Office Hours: Sun: 3:00  4:00 PM 

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. 

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. 

For further reading, see







