Ring Homomorphisms and Ideals

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Related lectures (32)

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Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Idempotent Elements and Central Orthogonal

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Rings and Fields

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

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Prime ideals and local rings

Covers the concept of prime ideals and local rings, emphasizing their importance.

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.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Symbolic Powers: Interpretation and Applications

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Chinese Remainder Theorem

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Irreducible Factors and Noetherian Rings

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