Examples
- Any division ring (including any field) is a near-field.
- The following defines a (right) near-field of order 9. It is the smallest near-field which is not a field.
- Let be the Galois field of order 9. Denote multiplication in by ' '. Define a new binary operation ' · ' by:
- If is any element of which is a square and is any element of then .
- If is any element of which is not a square and is any element of then .
- Then is a near-field with this new multiplication and the same addition as before.
- Let be the Galois field of order 9. Denote multiplication in by ' '. Define a new binary operation ' · ' by:
Read more about this topic: Near-field (mathematics)
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