Concept

Total ring of fractions

Related lectures (16)

Explores operations on ideals and structure theorems in commutative rings.

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Irreducible Polynomials and Finite Fields

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

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Algebraic Geometry: Rings and Bodies

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

Field of Fractions: Definition and Properties

Covers the definition and properties of a field of fractions.

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.

Rings and Fields: Principal Ideals and Ring Homomorphisms

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

Rational Numbers Construction

Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.

Properties of Euclidean Domains

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

Construction of Quotient Rings

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

Decimal Numbers

Explains the conversion process from fractions to decimal numbers and vice versa.

Real Numbers: Properties and Operations

Covers the properties and operations of real numbers, including divisibility rules and the concept of irreducible fractions.

Ring Theory: Definitions and Examples

Introduces ring theory, covering definitions, examples, and subrings criteria.

Rational Numbers: Amplification and Simplification

Covers rational numbers, amplifying and simplifying fractions, and calculating values.

Chinese Remainder Theorem: Rings and Fields

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