Field Properties: Irreducibility and Units

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

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

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

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

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Discusses irreducible factors in rings and the properties of Noetherian rings.

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

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

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

Covers the operations in rings, ideals, classes, and quotient rings.