Lectures related to Quotient ring

Construction of Quotient Rings

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

Chinese Remainder Theorem: Rings and Fields

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

Ring Operations: Ideals and Classes

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

Principal Ideal Domains: Structure and Homomorphisms

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

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Ring Homomorphisms and Ideals

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

Algebraic Geometry: Rings and Bodies

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

Properties of Division

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

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.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Amalgams: Group Pushouts

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

The Coordinate Ring of a Linearly Reductive Group

Covers the properties of the coordinate ring of a linearly reductive group.

Ring of Polynomials: Coefficients and Multiplication

Covers the ring of polynomials, focusing on coefficients and multiplication.

Polynomials: Definition and Operations

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

Algebraic Quotients

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

Well Pointed Spaces and Wedge

Discusses well pointed spaces, neighborhoods, wedges, examples, and the universal property of the quotient.

Irreducible Polynomials and Finite Fields

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

Algebra Review: Rings, Fields, and Groups

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

Group Presentation of S3

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