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Concept

Ideal (order theory)

Related lectures (31)

Ideals and PPCM

Covers the concept of ideals in polynomial rings and their properties.

Mathematical structures: selected topics

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Form and Stability of Arches: Cable and Arc

Discusses the form and stability of arches, emphasizing shape importance and load effects.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Ring Operations: Ideals and Classes Log in to Mediaspace to watch this video

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

Idempotent Elements and Central Orthogonal Log in to Mediaspace to watch this video

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Localization and Ideals Log in to Mediaspace to watch this video

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

Chinese Idempotent Constructions and Properties Log in to Mediaspace to watch this video

Explores Chinese idempotent constructions and their properties, including ideals and product characterization.

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.

Generators of Ideals Log in to Mediaspace to watch this video

Explores the calculation of generators of ideals and their significance in mathematical operations.

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.

Prime ideals and local rings Log in to Mediaspace to watch this video

Covers the concept of prime ideals and local rings, emphasizing their importance.

Irreducible Factors and Noetherian Rings Log in to Mediaspace to watch this video

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Factorisation in Dedekind Ring Log in to Mediaspace to watch this video

Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.

Algebraic Geometry: Localization and Prime Ideals Log in to Mediaspace to watch this video

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Ring Constructions: Structure Theorems Log in to Mediaspace to watch this video

Explores operations on ideals and structure theorems in commutative rings.

Rankine Cycles: Basics and Energy Balances Log in to Mediaspace to watch this video

Covers the basic concept of Rankine cycles, energy balances, improvements, and limitations.

Chinese Remainder Theorem: Rings and Fields Log in to Mediaspace to watch this video

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

Local Rings and Residues Log in to Mediaspace to watch this video

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Affine Algebraic Sets Log in to Mediaspace to watch this video

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.