Construction of Quotient Rings

Related lectures (36)

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

Covers the concept of ideals in polynomial rings and their properties.

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

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

Explores operations on ideals and structure theorems in commutative rings.

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

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

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

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

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

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

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

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

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

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

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

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

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

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

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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