LYCOS RETRIEVER 
Field (Mathematics)
built 656 days ago
The requirement 0 ≠ 1 ensures that the set which only contains a single zero is not a field. Directly from the axioms, one may show that (F, +) and (F - {0}, *) are commutative groups and that therefore (see elementary group theory) the additive inverse -a and the multiplicative inverse a-1 are uniquely determined by a. Furthermore, the multiplicative inverse of a product is equal to the product of the inverses:
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