Field

Definition

An algebraic structure consisting of a set $R$ equipped with two binomial operations: addition($+$) and multiplication($\cdot$) such that the following conditions hold.

• $R$ is an Abelian Group under addition.
• $R$ is Abelian Group under multiplication.
• Multiplication is distributive with respect to addition. $\forall r,s,t\in R:[r\cdot (s+t)=(r\cdot s)+(r\cdot t)]\wedge [(s+t)\cdot r=(s\cdot r)+(t\cdot r)]$

A commutative division Ring