| 释义 |
field of fractions If R is an integral domain, then a field of fractions F can be defined which naturally contains R. The field F is the set of equivalence classes of (r1,r2), where r1,r2 ϵ R and r2 ≠ 0 under the relation (r1,r2) ∼(s1,s2) if r1s2 = r2s1. The equivalence class of (r1,r2) can be identified with r1/r2, so that (r,1) can be identified with rϵR. The field of fractions of ℤ is ℚ with (4,8) and (–2,–4) both identified with ½.
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