 Field (mathematics)

A ring where multiplication is commutative and there is always an inverse.

A field can be seen as an Abelian group that has two group operations defined on it: addition and multiplication.

And then, besides each of the two operations obeying the group axioms individually, and they are compatible between themselves according to the distributive property.

Basically the nicest, least restrictive, 2-operation type of algebra.

Examples:

In mathematics, a **field** is a set equipped with two binary operations that generalize the arithmetic of rational numbers. These operations are typically called addition and multiplication, and they must satisfy certain properties. Specifically, a field is defined as follows: 1. **Closure**: For any two elements \( a \) and \( b \) in the field, both \( a + b \) and \( a \cdot b \) are also in the field.