Properties of Euclidean Domains

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Finite Fields and Group Theory

Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].

Congruence Relations in Rings

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

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Ring Operations: Ideals and Classes

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

Irreducible Factors and Noetherian Rings

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

Division Rings and Ideals

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Euclidean Algorithm

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

Cyclic Subspace Decomposition

Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.

Ramification and Structure of Finite Extensions

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.