What is Field?

A ring R is called a field if it is 

1. Commutative
2. Has unit element,
3. And each non-zero elements possess a multiplicative inverse.

Example of Fields

Some of the examples of fields are:

• The set R of all real numbers is a field as R is a commutative ring with unity and each non-zero element has a multiplicative inverse. 
• The set of all fractions a/b​ where a and b are integers and b ≠ 0 under addition and multiplication.
• Set of all decimal expansions, including both rational and irrational numbers under addition and multiplication.

In this article, we will discuss and prove that every field in the algebraic structure is an integral domain. A field is a non-trivial ring R with a unit. If the non-trivial unitary ring is commutative and each non-zero element of R is a unit, so the non-empty set F forms a field with respect to two binary operations. and +.