Abstract Algebra II
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There is no required textbook. All lecture notes will be posted here. For further reading I recommend Michael Artin's Algebra, Charles C. Pinter's Book of Abstract Algebra and John Stillwell's Elements of Algebra.
Office Hours: TBA Here is the syllabus. | ||
| Course Notes (and here are the old notes from Algebra I) | ||
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| Item | Date | Information |
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Homework 1 Solutions in the Notes |
Fri Feb 1 |
The Classical Problem of Algebra Definition of Fields and Subfields The Lattice of Subfields The Galois Group The Fundamental Theorem of Galois Theory |
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Homework 2 Solutions in the Notes |
Fri Feb 15 |
Rings and Subrings Ring Homomorphisms Ideals and Quotient Rings Correspondence and Isomorphism Theorems Descartes' Factor Theorem Z and F[x] are PIDs |
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Exam 1 Solutions |
Wed Feb 20 | |
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Homework 3 Solutions in the Notes |
Fri Mar 8 |
Irreducible and Prime Elements PID implies UFD The Minimal Polynomial Kronecker's Theorem Existence of Splitting Fields |
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Homework 4 Solutions in the Notes |
Mon Apr 1 |
Working With Irreducible Polynomials Cyclotomic Polynomials Existence and Uniqueness of Finite Fields Fundamental Theorem of Algebra |
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Exam 2 Solutions |
Fri Apr 5 | |
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Homework 5 Solutions in the Notes |
Fri Apr 26 |
The Finiteness Theorem The Splitting Field Theorem Artin's Fixed Field Lemma Characterization of Galois Extensions The Fundamental Theorem of Galois Theory |
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Exam 3 Solutions |
Fri May 3 | |