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单词 splitting field
释义
splitting field

Mathematics
  • Given a polynomial f(x) with coefficients from a field F, its splitting field K is the smallest field in which f(x) factorizes into linear factors. The splitting field is unique up to isomorphism. For example, the splitting field of x2+1 over ℚ is ℚ[i] as

    x2+1 = (xi)(x+i).


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