Division ring

Imagine you have a large pizza that you want to share with your friends. If the pizza is cut evenly into pieces, everyone can have an equal amount of pizza. But what if the pizza cannot be cut evenly into pieces? In this case, you cannot share the pizza fairly.

Similarly, in math, we have numbers that we can divide into equal parts, but some numbers cannot be divided into equal parts. These numbers are called "division rings." A division ring is a special type of mathematical object that acts like numbers but cannot be divided into equal parts.

Imagine you have a set of objects, and you want to divide them equally among your friends. If the objects can be divided evenly, you can do this easily. But if the objects cannot be divided equally, sharing them becomes difficult, just like with the pizza.

In math terms, division rings are sets of objects that can be multiplied and divided, just like numbers. However, not all division rings can be divided into equal parts. This means that sharing these objects equally is not always possible.

So, a division ring is a special type of mathematical object that behaves like numbers, but not all of them can be divided equally. It's like trying to slice a pizza that cannot be cut into equal pieces – it's challenging to share it fairly.