Associated prime
Imagine you have a big pack of crayons and you start to color a picture, but you only color some parts of it with specific colors. Those specific colors you use are called "prime colors".
Similarly, when we have a mathematical formula, we can break it down into smaller parts, called "factors". In some cases, we can identify certain factors as "prime factors", which means they can't be broken down any further.
Now, when we look at a mathematical object called a ring, it has different ways of breaking it down into factors. Some of these factors are called "associated primes". These associated primes are like the "prime colors" we talked about earlier, but for rings instead of pictures.
So, just like how you can have multiple "prime colors" in a picture (like red, blue, and green), a ring can have multiple associated primes. And just like how the prime colors you choose can affect the overall look of a picture, the associated primes you identify in a ring can affect the overall properties and behavior of the ring.
Similarly, when we have a mathematical formula, we can break it down into smaller parts, called "factors". In some cases, we can identify certain factors as "prime factors", which means they can't be broken down any further.
Now, when we look at a mathematical object called a ring, it has different ways of breaking it down into factors. Some of these factors are called "associated primes". These associated primes are like the "prime colors" we talked about earlier, but for rings instead of pictures.
So, just like how you can have multiple "prime colors" in a picture (like red, blue, and green), a ring can have multiple associated primes. And just like how the prime colors you choose can affect the overall look of a picture, the associated primes you identify in a ring can affect the overall properties and behavior of the ring.