Field

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Definition

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

• Every non-zero element of $F$ has a multiplicative inverse in $F$

Every field is also an Integral domain

Proof of claims

[Expand]

• Every field is an Integral domain

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See also

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