Ring of restricted power series

Okay, kiddo! So let's start by talking about rings. A ring is just a fancy name for a set of numbers that you can do some special things with, like adding and multiplying them together. Kind of like how you might add and multiply your toys together!

Now, a power series is when you add up lots of really tiny numbers together to make a bigger number. Imagine you have a giant pile of tiny Lego pieces, and if you put them together just right, you can make a really cool castle! That's kind of what a power series is like.

So a ring of restricted power series is just a special kind of ring that's made up of all these power series. But there's a catch! The power series in this ring have to follow some rules, like they can only have a certain amount of terms and the terms have to get smaller and smaller as you go on.

Think of it like building a tower out of blocks, but each block has to be smaller than the one below it, and you can only use a certain number of blocks. That's kind of like what a power series in a ring of restricted power series is like.

Overall, a ring of restricted power series is just a special set of numbers that you can add and multiply together, but the numbers have to be arranged in a very particular way, kind of like building a tower out of blocks!