Quotient ring

Okay kiddo, imagine you have a big bag of marbles. Some marbles in the bag are really special, and the others are just regular marbles. You decide that you want to play with only the special marbles and put the regular marbles aside.

Now, the special marbles all have something in common - they have a number on them that is divisible by 5. So, you take all the special marbles and put them into a separate bag. This new bag of special marbles is like a quotient ring.

A quotient ring is kind of like a bag of marbles that only includes some of the original marbles. But, instead of choosing marbles based on a divisible number, a quotient ring is made up of things like mathematical equations or polynomials that all have something in common.

So, instead of playing with all the marbles in the original bag, you create a subset (a smaller group) of the special marbles that follows a certain rule. The remaining marbles in the original bag are like the regular elements that were left out of the quotient ring.

Overall, a quotient ring is just a subset of a bigger collection of things that all have something in common. It's like having a special club within a larger group.