Algebraic Geometry: Rings and Bodies

Related lectures (32)

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

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

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

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

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

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

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

Covers polynomials, their operations, division theorem, and provides illustrative examples.