Concept

Ring homomorphism

Related lectures (31)

Principal Ideal Domains: Structure and Homomorphisms

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

Chinese Remainder Theorem: Rings and Fields

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

Ring Homomorphisms and Ideals

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Chain Maps: Homotopy Invariance

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Group Homomorphisms

Explores group homomorphisms, Euler's phi function, and group products.

Polynomials on a Field: Basics and Operations

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

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Group Homomorphisms

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Dimension Theory of Rings

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

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.

Quotient Groups and Homomorphisms

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.

Algebra of Matrices: Properties and Fields

Covers the properties of the algebra of matrices and related concepts.

Ideals in Commutative Rings

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

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Push-out: Categorical Perspective on Quotients

Explores the concept of push-out in group homomorphisms.

Congruence Relations in Rings

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