Explore the algebra of rings and fields through 24 interactive demonstrations. From ring axioms and ideals to finite field construction, unique factorization, and real-world applications in cryptography and coding theory.
See also: Number Theory for the rings of integers and their unique factorization, Galois Theory for the field extensions and their automorphism groups, and Algebraic Geometry for the geometric meaning of every commutative ring.
Ring axioms, commutativity, zero divisors, and key examples
Principal, prime, and maximal ideals with lattice diagrams
Coset construction, polynomial quotients, and the CRT
Division algorithm, GCD, and irreducibility testing
GF(p), GF(p^n) construction, and the Frobenius map
Gaussian integers, factorization failure, and norms
Kernels, images, and the First Isomorphism Theorem
Reed-Solomon codes, RSA cryptography, and algebraic curves