Lecture

Fractions of Rings

Related lectures (32)

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

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

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

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

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

Explores operations on ideals and structure theorems in commutative rings.

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

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

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

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

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

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

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

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

Explores the calculation of generators of ideals and their significance in mathematical operations.

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

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

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