Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Quotient (universal algebra)

Related lectures (32)

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

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

Explores the properties of division in natural numbers and its relation to multiplication.

Covers binary operations, including addition and multiplication of integers represented in binary form.

Explores quotient groups, left classes decomposition, group structure, and unique homomorphisms.

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Covers the properties of division in integers and the relationship between divisibility and unique quotients.

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Introduces equivalence classes for decomposing a set into subsets of equivalent elements, defining the quotient set X/~.

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

Covers the concept of algebraic quotients in the context of a-variety.

Covers the concept of Kähler differentials, exploring linearity, construction, and B-linearity in algebraic geometry.

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

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.