Polynomial Rings and Irreducibility Criteria

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Irreducible Polynomials and Finite Fields

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

Euclidean Algorithm

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Rings and Fields: Principal Ideals and Ring Homomorphisms

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

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation.

Rings and Ideals

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Algorithm Basics: Ingredients

Covers algorithms, data, loops, control structures, and the Euclidean algorithm.

Properties of Euclidean Domains

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

Polynomials: Definitions and Operations

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