Finite Fields and Group Theory

Related lectures (31)

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Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Covers the concept of ideals in polynomial rings and their properties.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

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

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.