Ignore if not innervoid

[cube]

@InnerVoid PhD man help me with my math hw

I cannot for the life of me understand this prime ideal shit, why are they called "prime" but have nothing to dowith prime numbers, but just some random ass rule, and what are they even used for

 

[emeraldglass]

Prime ideals in ring theory have nothing to do with prime numbers. The term “prime” here refers to a different kind of “primeness” related to algebraic structures. So, while they share the name, their underlying concepts and applications are distinct.

Prime numbers are positive integers greater than 1 that have no positive divisors other than 1 and themselves. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. They play a important role in number theory and have applications in cryptography, algorithms, and more.


In ring theory (the picture above), the term "prime" refers to a specific concept regarding ideals within a mathematical structure called a ring, denoted by R. An ideal of R is a subset that meets certain criteria. A prime ideal is one that has the property that if the product of two elements, denoted as a and b, belongs to the ideal (ab ∈ I), then either a or b individually must also belong to the ideal (a ∈ I or b ∈ I).

This concept is comparable to the behavior of prime numbers in integer arithmetic.