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Concept

Ring of integers

Related lectures (32)

Integers and Rings Log in to Mediaspace to watch this video

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Galois Theory: Dedekind Rings Log in to Mediaspace to watch this video

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Fermat's Equation: Integral Solutions and Gaussian Integers Log in to Mediaspace to watch this video

Discusses Fermat's equation and Gaussian integers' properties.

Closure Conversion: Representation and Transformation Log in to Mediaspace to watch this video

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.

Linear Algebra: Integers Log in to Mediaspace to watch this video

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

Dimension theory of rings Log in to Mediaspace to watch this video

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Logic and Proof Techniques Log in to Mediaspace to watch this video

Covers integers, rationals, logic, proof techniques, functions, and relations using examples and truth tables.

Functions and Integers Log in to Mediaspace to watch this video

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Function Composition and Integers Log in to Mediaspace to watch this video

Covers function composition and integers, including properties and examples.

Integers: Sets, Maps, and Principles Log in to Mediaspace to watch this video

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Number Theory: Operations and Equivalence Log in to Mediaspace to watch this video

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Algebraic Structures and Integers Log in to Mediaspace to watch this video

Covers algebraic structures, crystal planes with Miller indices, and coprime numbers.