# field

A set \(X\) with two operations, addition and \(+\) and multiplication \(\cdot\), such that:

- addition is an abelian group (algebra) with identity element 0
- multiplication is an abelian group with identity 1
- multiplication distributes over addition

### 0.1. ring

- A related structure, which also has \(+\) and \(\cdot\)
- addition is an abelian group with identity element 0
- multiplication is a monoid (see the note group (algebra)) with identity element 1
- multiplication distributes over addition