Lecture

Factorisation in Principal Ideal Domains

Description

This lecture covers the factorisation in Principal Ideal Domains (PIDs), where every prime ideal is maximal. It explores the unique factorisation of ideals, the ring Z[i], and the concept of Principal Ideal Domains. The lecture also delves into the relationship between sums of two squares and the properties of prime numbers.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related lectures (44)
Dedekind Rings: Theory and Applications
Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Dimension theory of rings
Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Additivity of Dimension & Height
Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.