Chinese Remainder Theorem and Polynomial Rings

Related lectures (30)

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Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Covers commutative groups and their significance in cryptography.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.