Quotient (universal algebra)

Related lectures (32)

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

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

Explores the symmetric group, emphasizing cycle notation and group properties.

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

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

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

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Covers the construction of push-outs in the category Ens and philosophical concepts of universality and co-universality.

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

Covers equivalence classes, decomposition of sets, and constructing quotient sets.

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/~.

Page 2 of 2