Concept

Integral domain

Related lectures (32)

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.

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

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

Covers the definition and properties of a field of fractions.

Covers extending domains, leading coefficients, and valid extensions.

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

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

Covers the properties of harmonic functions, focusing on the mean value property and the maximum principle.

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

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

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

Discusses integral domains, abelian groups, invertibility, zero divisors, prime elements, and group classification.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

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

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

Explores regularity, divisors, prime divisors, and uniqueness in algebraic geometry.

Covers the heat equation for diffusion and conservation of thermal energy.