| 单词 | field |
| 释义 | field (x) For each non-zero a there is an element a−1 such that a−1a = 1. (The axiom numbering here follows on from that used for ring and integral domain.) From the defining properties of a field, Axioms (i)–(viii) and Axiom (x), it can be shown that ab = 0 only if a = 0 or b = 0. Thus Axiom (ix) holds, and so any field is an integral domain. Familiar examples of fields are the rational numbers ℚ, the real numbers R and the complex numbers ℂ, each with the usual addition and multiplication. Another example is ℤp, the integers with addition and multiplication modulo p, where p is prime. See also Galois field. |
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