Rings: Operations and Ideals

Related lectures (32)

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

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Explores operations on ideals and structure theorems in commutative rings.

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

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

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

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

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

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