Math
Abstract Algebra II
Train on Abstract Algebra II with 300 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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Preview a course problem
See a problem from Abstract Algebra II before you begin.
Course topics
Course topics
Rings, ideals, quotient rings, and homomorphisms
Domains, divisibility, and factorization
Polynomial rings and irreducibility
Modules and finitely generated modules over a PID
Algebraic field extensions and minimal polynomials
Finite Galois theory
Practice problems
Try a few Abstract Algebra II problems, each with a hint.
- Gaussian integers form a subring Free with an accountRings, ideals, quotient rings, and homomorphisms
- Kernel of evaluation at a point Free with an accountRings, ideals, quotient rings, and homomorphisms
- Divisibility is transitive Domains, divisibility, and factorization
- Lcm from prime exponents Domains, divisibility, and factorization
- Content and primitive part Polynomial rings and irreducibility
- Reciprocal polynomials preserve irreducibility Polynomial rings and irreducibility
- Kernels and images are submodules Modules and finitely generated modules over a PID
- When finitely generated torsion means finite Modules and finitely generated modules over a PID
- A cubic extension has no quadratic intermediate field Algebraic field extensions and minimal polynomials
- A quartic whose splitting field is only quadratic Finite Galois theory