301CRS Algebra 3

CMI, Aug-Nov 2025, Clare D’Cruz
Artin (2011), Dummit & Foote (2004), Aluffi (2009) (Errata), Lang (2002), Hungerford (1974), Conrad’s expository papers

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Intro to Category Theory
Intro to Ring Theory

Lectures

LEC ALG3 1 ✅ Ring homomorphisms, polynomial rings, products and coproducts
LEC ALG3 2 ✅ Quotients and ideals
LEC ALG3 3 ✅ Modules
LEC ALG3 4 ✅ Quotients of polynomial rings, prime and maximal ideals, power series rings
LEC ALG3 5 ✅ Radicals
LEC ALG3 6 ✅ Krull’s theorem, Chinese remainder theorem
LEC ALG3 7 ✅ Irreducible and prime elements
LEC ALG3 8 ✅ Ring of fractions
LEC ALG3 9 ✅ Euclidean domains and unique factorization domains
LEC ALG3 10 ✅ Gauss’s Lemma
LEC ALG3 11 Gaussian primes
LEC ALG3 12 More on factoring
LEC ALG3 13 Eisenstein’s Criterion
LEC ALG3 15 ✅ Field extensions, algebraic elements, minimal polynomials
LEC ALG3 16 More on field extensions
LEC ALG3 17
LEC ALG3 18
LEC ALG3 19

Stuff I’ll look at later
Quadratic integer rings

Tutorials

TUT ALG3 1
TUT ALG3 2
TUT ALG3 3
TUT ALG3 4
TUT ALG3 5
TUT ALG3 6
TUT ALG3 7

TST ALG3 Midsem

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References

Aluffi, P. (2009). Algebra: Chapter 0. American Mathematical Society.

Artin, M. (2011). Algebra (2. ed). Pearson Education, Prentice Hall.

Dummit, D. S., & Foote, R. M. (2004). Abstract Algebra (3rd ed). Wiley.

Hungerford, T. W. (1974). Algebra (Vol. 73). Springer New York. https://doi.org/10.1007/978-1-4612-6101-8

Lang, S. (2002). Algebra (Vol. 211). Springer New York. https://doi.org/10.1007/978-1-4613-0041-0