Rings

A Ring is a tuple \((\mathbb{R}, +, \times, 0,1)\), where \(\mathbb{R}\) is the set of elements, \(+\) is the addition operator, \(\times\) is the multiplication operator, \(0\in \mathbb{R}\) is the additive identity, and \(1\in \mathbb{R}\) is the multiplicative identity. \(\mathbb{R}\) must have the following properties:

1. \((\mathbb{R}, +, 0)\) forms a group.
2. \(\times\) is associative.
3. \(\times\) distributes over \(+\).