Concept

Principal ideal

Related lectures (31)

Ideal Class Group Relations

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

The classical Lie algebras

Covers the classical Lie algebras, focusing on calculations and dimensions.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

The Discriminant and Ideal Class Group in Mathematics

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

The Ring of Eisenstein Integers: Properties and Applications

Covers the properties of the ring of Eisenstein integers and its submodule structure.

Hermite-Minkowski Theorems: Number Fields and Ideal Classes

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Principal Ideal Domains: Structure and Homomorphisms

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

Rings and Modules

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

Discrete Valuation Rings

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Chinese Remainder Theorem: Euclidean Domains

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Dedekind Rings: Factorisation and Ideal Class Group

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

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.

Irreducible Factors and Noetherian Rings

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

Ziegernichels Tuning

Covers Ziegernichels tuning, a method to quickly tune PID coefficients for stable and unstable systems.

Factorisation in PIDs

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Logarithmic Embedding in Number Fields

Explores the properties and applications of logarithmic embeddings in number fields.

Number Fields: Embeddings and Ideal Classes

Covers the embeddings of number fields and ideal classes with proofs and examples.

Algebra: Fundamental Theorem

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

Lag Compensator Design

Explores lag compensator design in control systems, emphasizing phase margin and steady-state error improvement through practical examples.

Integral Domains: Factorisation and Noetherian Rings

Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.