Chinese Remainder Theorem: Rings and Fields

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Related lectures (32)

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Division Rings and Ideals

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

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Division Rings and Ideals

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

Idempotent Elements and Central Orthogonal

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

Construction of Quotient Rings

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

Polynomials, Division, and Ideals

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

Irreducible Factors and Noetherian Rings

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

Rings and Ideals

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Chinese Remainder Theorem and Euclidean Domains

Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

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.

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