Lectures related to Quotient (universal algebra)

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

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

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

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.

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 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.

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

Covers rings and modules, emphasizing color codes and homological algebra concepts.

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

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

Explores examples of algebraic quotients using invariance maps and discriminant.

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

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

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