Factorization | Commutative algebra | Algebraic number theory
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are at least three other characterizations of Dedekind domains that are sometimes taken as the definition: see . A field is a commutative ring in which there are no nontrivial proper ideals, so that any field is a Dedekind domain, however in a rather vacuous way. Some authors add the requirement that a Dedekind domain not be a field. Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial modifications for the case of fields. An immediate consequence of the definition is that every principal ideal domain (PID) is a Dedekind domain. In fact a Dedekind domain is a unique factorization domain (UFD) if and only if it is a PID. (Wikipedia).
Here we show a quick way to set up a face in desmos using domain and range restrictions along with sliders. @shaunteaches
From playlist desmos
Tv Reclame van de De Belastingdienst Telsell parodie
From playlist awareness
What Is a radian? Coffee โ๏ธ + Desmos ๐ this AM = https://www.desmos.com/calculator/bcgjcpci3k. Also added to https://teacher.desmos.com/activitybuilder/custom/60742b18afd8ae0d274b6efb.
From playlist Desmos Activities, Illustrations, and How-To's
DesmosLIVE: An Exploration of Desmos + Mathalicious
Kate Nowak of Mathalicious explores a few Mathalicious lessons with Desmos
From playlist Desmos LIVE
Abstract Algebra | A PID that is not a Euclidean Domain
We present an example of a principal ideal domain that is not a Euclidean domain. We follow the outline described in Dummit and Foote. In particular, we show that an integral domain D is a PID if and only if it has a Dedekind-Hasse Norm and that every Euclidean domain has a universal side
From playlist Abstract Algebra
Dedekind domains: Introduction
This lecture is part of an online graduate course on commutative algebra, and is an introduction to Dedekind domains. We define Dedekind domains, and give several examples of rings that are or are not Dedekind domains. This is a replacement video: as several alert viewers pointed out, t
From playlist Commutative algebra
5 Best Practices In DevOps Culture | What is DevOps? | Edureka
๐ฅ๐๐๐ฎ๐ซ๐๐ค๐ ๐๐๐ฏ๐๐ฉ๐ฌ ๐๐จ๐ฌ๐ญ ๐๐ซ๐๐๐ฎ๐๐ญ๐ ๐๐ซ๐จ๐ ๐ซ๐๐ฆ ๐ฐ๐ข๐ญ๐ก ๐๐ฎ๐ซ๐๐ฎ๐ ๐๐ง๐ข๐ฏ๐๐ซ๐ฌ๐ข๐ญ๐ฒ: https://www.edureka.co/executive-programs/purdue-devops This tutorial explains what is DevOps. It will help you understand some of its best practices in DevOps culture. This video will also provide an insight into how different
From playlist Webinars by Edureka!
Schemes 39: Divisors and Dedekind domains
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we describe Weil and Cartier divisors for Dedekind domains, showing that they correspond to the two classical ways of defining the class group
From playlist Algebraic geometry II: Schemes
(English Version: https://www.youtube.com/watch?v=DosqbEy8ecY) http://www.nucleusinc.com/ - ่ฟไธชไธ็ปดๅจ็ปไป็ปไบๅณ้ซๅ ณ่็ๅ จ้ซๅ ณ่็ฝฎๆขๆฏใ่ฏฅๆๆฏๅ ๆฌๅๅผใ้ฒๅบ้ซๅ ณ่ใๆพ็ฝฎ้ซ่ผไฟฎๅคๅไฝ๏ผ็ช๏ผใๅฒๆๅ็็่กๆฒๅคดใๆพ็ฝฎ่ก้ชจๅคดๅไฝ๏ผ็๏ผใ
From playlist ๅจไธญๅฝๅปๅญฆๅจ็ป
A crash course in Algebraic Number Theory
A quick proof of the Prime Ideal Theorem (algebraic analog of the Prime Number Theorem) is presented. In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number of prime idea
From playlist Number Theory
Schnitt einer Ebene mit einer Geraden
Quickstart fรผr die Desktop Version Beispiel 5: Schnitt einer Ebene mit einer Geraden
From playlist Quickstart fรผr die Desktop Version
Desmos Copy and Paste Data Issue
I am loving the desmos scavenger hunt and am learning so much! https://docs.google.com/document/d/1_ZqgHZg41LqteL8wDFgmtdP_twlwEDZ9Ma4cP-HsSqU/edit I just finished intermediate #6 and encountered an issue. Wondering what is happening here.
From playlist desmos
[ANT13] Dedekind domains, integral closure, discriminants... and some other loose ends
In this video, we see an example of how badly this theory can fail in a non-Dedekind domain, and so - regrettably - we finally break our vow of not learning what a Dedekind domain is.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Pete Clark, The torsion subgroup of a CM elliptic curve over a number field
VaNTAGe seminar, June 22, 2021 License CC-BY-NC-SA
From playlist Modular curves and Galois representations
From playlist Atelier PARI/GP 2016
Difficulties with Dedekind cuts | Real numbers and limits Math Foundations 116 | N J Wildberger
Richard Dedekind around 1870 introduced a new way of thinking about what a real number `was'. By analyzing the case of sqrt(2), he concluded that we could associated to a real number a partition of the rational numbers into two subsets A and B, where all the elements of A were less than al
From playlist Math Foundations
Second part to this video: http://youtu.be/shEk8sz1oOw More links & stuff in full description below โโโ If the highest power of a function or polynomial is odd (e.g.: x^3 or x^5 or x^4371) then it definitely has a solution (or root) among the real numbers. Here's a nice proof demonstrate
From playlist David Eisenbud on Numberphile
Kaiser, Bรผrger und Genossen, Teil 1: Der Friede
Geschichte des wilhelminischen Kaiserreichs in zwei Teilen Teil 1 "Der Friede" behandelt Verfassungs-, Wirtschafts-, Sozial-, Technik- und Kulturgeschichte - Image des Kaiserreichs: Militarismus, forsches Auftreten Kaiser Wilhelms II. - Fรถderalismus und regionale Verschiedenheit der Bund
From playlist Kaiserzeit
Four Step Recovery Programme for Division by Zero Deniers
Division by zero has been possible since 1957. LINKS: Transmathematica Channel https://youtube.com/channel/UC2ro5bMjox_KhU-UbUvx7jQ Rehab Playlist https://youtube.com/playlist?list=PL2qvIMkhqXu036a0M_TLAryIqjiRO6OKs History of division by zero https://doi.org/10.36285/tm.37 Suppes htt
From playlist Summer of Math Exposition Youtube Videos