What is the difference between a group and ring in mathematics?
In mathematics, a group is a set equipped with an associative binary operation (usually written as ·) which has an identity element (`e` such that `x·e = x = e·x`), in which every element `x` has an inverse `x^{-1}` such that `x · x^{-1} = e = x^{-1} x`.

In contrast, a ring is an abelian group (a group where `a + b = b + a`. In this case, the group operation is written as `+` instead of `·`, and `e` is called `0`) equipped with a second associative operation called multiplication. The symbol · usually denotes the ring multiplication operation, and + is used for the group operation.

Multiplication must have an identity element, usually called `1`, making a ring a monoid under multiplication.

Also, multiplication should distribute over group operations. `a · (b + c) = (a·b) + (b·c)` and `(b + c) · a = (b·a) + (c·a)`.

So, rings are groups with extra structure that allow them to support arithmetic.
Awesome, thank you! That seems to make sense to me!
You're welcome! If you have any more questions or need further clarification, just let me know!
Can you expand on the previous topic?