CMI, Jan-Apr 2026, Manoj Kummini
Milne (n.d.), Lang (2002), Artin (2011), Aluffi (2009) Chapter 6, @isaacsAlgebraGraduateCourse2009
Topics:
- module theory (mostly over commutative rings): Hom and tensor; projective and injective modules. Structure theorem of modules over PIDs. application to linear operators.
- Galois theory: splitting fields, field automorphisms, fixed fields, Galois extensions, normal and separable extensions, examples.
References
Aluffi, P. (2009). Algebra: Chapter 0. American Mathematical Society.
Artin, M. (2011). Algebra (2. ed). Pearson Education, Prentice Hall.
Lang, S. (2002). Algebra (Vol. 211). Springer New York. https://doi.org/10.1007/978-1-4613-0041-0
Milne, J. S. (n.d.). Fields and Galois Theory.