Integral domain
A ring R is called an integral domain if it is
- Commutative
- Has unit element
- And has no zero divisors.
Example: The set Z of all integers is an integral domain as Z is a commutative ring with unity and also does not possess zero divisors.
Prove that Every Field is an Integral Domain
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 +.
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