Ring Theory: Definitions and Examples

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Related lectures (32)

Page 2 of 4

Congruence Relations in Rings

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

Integrity in Algebra

Explores the properties of commutative rings and integral domains in algebra.

Construction of Quotient Rings

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

Ring Theory: Morphisms and Isomorphisms

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Idempotent Elements and Central Orthogonal

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

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.

Ideals in Commutative Rings

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

Rings and Fields: Principal Ideals and Ring Homomorphisms

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

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.