Ideal in Ring

Historical Background:

Ideal (理想) was a by-product by mathematicians in the 350-year proof of the 17CE Fermat’s Last Theorem, wherein they found a violation of the existing “Fundemental Law of Arithmetic” (Unique Prime Factorization) . Since it is a Law, there must be an alternative ideal number to satisfy it, hence the birth of the “Ideal”.

Read here: the raison d’être of Ideal : What is an Ideal ?

Note:

Why Integer (Z) is called “Ring” (Dedekind coined it using the German word “Der Ring”) ? because
{1, 2, … , 11, 12 = 0} is clock number “Z/12Z” like a Ring-shaped Clock 🕜

Application:

The ancient “Chinese Remainder Theorem” (aka 韩信点兵 ) since 200 BCE is explained by 19CE Ideal Theory.

[Solve] : “The Problem of 6 Professors

Ideal = “Whatever inside multiplies outside, still comes back inside.”

Ring Examples:

  1. Integers Z
  2. Polynomial with coefficients in Real number , or Complex number, or Matrix (yes!)
  3. Infinite Ring
  4. Finite Ring (Z/nZ )
  5. Z/pZ = Field (p is prime)

Reference:

33 short videos on the scariest Math subject in universities (France, USA, China, Singapore,… ) “Abstract Algebra” made simple by this charming lecturer.

What is Harmony OS? Huawei’s “Android rival” explained!


https://www.androidauthority.com/huawei-harmony-os-1030848/

1. Harmony OS : Micro-Kernel for ‘1+8+N’ IoT devices

2. ARK Compiler for Android code compatibility (Java, C/C++, Kotlin, JS), yet 60% faster

3. AppGallery : confirmed ‘Yes’ for Facebook, WhatsApp, Insragram. Next ? will be Google Mobile Services (YouTube, Gmail, Google Map, Google Playstore )

4. HMS (Huawei Mobile Services) : $1 billion Apps development fund by Huawei