MATH 5112: Algebra 2
Lecture - 4 credits
- Continues MATH 5111.
- Topics include groups, such as subgroups, normal subgroups, homomorphism of groups, abelian groups, solvable groups, free groups, finite p-groups, Sylov theorem, permutation groups, and the sign homomorphism; rings, such as homomorphism, ideals, quotient rings, integral domains, extensions of rings, unique factorization domain, Chinese remainder theorem, and Gauss's lemma; and modules, such as homomorphism, submodules, quotient modules, exact sequence, and structure of finitely generated modules over principal ideal domains.
- Examples include abelian groups and Jordan canonical form.
- Also covers representations of finite groups, group rings and irreducible representations, Frobenius reciprocity, Maschke theorem and characters of finite groups, and dual groups.
- Requires permission of instructor and head advisor for undergraduate students.
Continues MATH 5111. Show more.