Ring Operations: Ideals and Classes

Related lectures (32)

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Explores the construction of quotient rings and the properties of well-defined operations within rings.

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

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

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

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Covers the operations and properties of rings, focusing on ideals and quotients.

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

Introduces the definition and examples of A-modules, including sub-modules and ideals.

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

Covers ideals, representations, modules, and maximal ideals in associative algebras.