Field

Definition

A field is a ring, [ilmath]F[/ilmath], that is both commutative and has unity with more than one element is a field if:

• Every non-zero element of [ilmath]F[/ilmath] has a multiplicative inverse in [ilmath]F[/ilmath]

Every field is also an Integral domain

Proof of claims

• Every field is an Integral domain

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See also

• Vector space
• Ring
• Integral domain
• Types of rings
• Characteristic of a ring