Fractional ideal

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Related lectures (32)

Ring Operations: Ideals and Classes

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

Irreducible Factors and Noetherian Rings

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

Ideals and PPCM

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

Hilberts Nullstellensatz and Ideals

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Dedekind Rings: Theory and Applications

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Principal Ideal Domains: Structure and Homomorphisms

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

Rankine Cycles: Basics and Energy Balances

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

Localization and Ideals

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

Galois Theory: Dedekind Rings

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

Idempotent Elements and Central Orthogonal

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

Chinese Idempotent Constructions and Properties

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

Chinese Remainder Theorem: Rings and Fields

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

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Ideal Class Group Relations

Covers the relations between the ideal class group and proper fractional ideals.

Fractions of Rings

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Generators of Ideals

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

Algebra: Fundamental Theorem

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

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