Quasi-finite field
Imagine you have a toy chest with a certain number of toys in it. Now let's say you want to play a game where you give one toy at a time to your friend until there are no more toys left in the chest. This game is like dividing a finite field into subfields.
Now, imagine you have a magic toy chest that has an infinite number of toys in it. You and your friend can play this game forever, and there will always be toys left in the chest. This magic toy chest is like a quasi-finite field.
A quasi-finite field is a field that is not finite, but its subfields are all finite. That means you can keep dividing the quasi-finite field into smaller subfields that are finite until you can't divide any further. This is different from a finite field, which cannot be divided any further.
So just like how you can't take any more toys out of a finite toy chest, you can't divide a finite field into any smaller subfields. But with a quasi-finite field, you can keep dividing it into smaller subfields as long as you want.
Now, imagine you have a magic toy chest that has an infinite number of toys in it. You and your friend can play this game forever, and there will always be toys left in the chest. This magic toy chest is like a quasi-finite field.
A quasi-finite field is a field that is not finite, but its subfields are all finite. That means you can keep dividing the quasi-finite field into smaller subfields that are finite until you can't divide any further. This is different from a finite field, which cannot be divided any further.
So just like how you can't take any more toys out of a finite toy chest, you can't divide a finite field into any smaller subfields. But with a quasi-finite field, you can keep dividing it into smaller subfields as long as you want.