Lectures related to Ideal (ring theory)

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

Idempotent Elements and Central Orthogonal

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

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

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.

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.

Algebraic Subsets of A^1

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

Galois Theory: Dedekind Rings

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

Generators of Ideals

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

Principal Ideal Domains: Structure and Homomorphisms

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

Chinese Idempotent Constructions and Properties

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

Fractions of Rings

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

Rankine Cycles: Basics and Energy Balances

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

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.

Ring Homomorphisms and Ideals

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

Chinese Remainder Theorem: Rings and Fields

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

Irreducible Factors and Noetherian Rings

Discusses irreducible factors in rings and the properties of Noetherian rings.

Regular Implicit Functions

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

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.