Factorisation in Principal Ideal Domains

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Division Rings and Ideals

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Finite Fields: Construction and Properties

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Factorisation in Dedekind Ring

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.

Ring Operations: Ideals and Classes

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

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Affine Algebraic Varieties: Zariski Topology

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

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.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.