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Lecture
Algebraic Geometry: Rings and Bodies
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Related lectures (57)
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Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.
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Polynomials and Endomorphisms
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Algorithms for Big Numbers: Z_n and Orders
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Division Polynomials: Theorems and Applications
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Decimal Expansion: Division and Periodicity
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Chinese Remainder Theorem: Rings and Fields
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Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Rings and Fields: Principal Ideals and Ring Homomorphisms
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Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Algebra Review: Rings, Fields, and Groups
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Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.
Properties of Euclidean Domains
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Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.
Congruence Relations in Rings
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Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.
Finite Fields: Construction and Properties
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Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Irreducible Polynomials and Finite Fields
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Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.
Properties of Euclidean Domains
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Covers the properties of Euclidean domains and irreducible elements in polynomial rings.
Polynomials on a Field: Basics and Operations
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Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.
Chinese Remainder Theorem and Euclidean Domains
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Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.
Polynomial Factorization: Field Approach
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Covers the factorization of polynomials over a field, including division with remainder and common divisors.
Polynomial Factorization over a Field: Eigenvalues
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Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.
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