The “fundamental theorem of algebra” for quaternions
The “fundamental theorem of algebra” for quaternions
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DOI：
10.1090/s0002-9904-1944-08125-1
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发表时间：
1944-04
影响因子：
1.3
通讯作者：
S. Eilenberg;I. Niven
中科院分区：
文献类型：
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作者：
S. Eilenberg;I. Niven
f 在 oo 处的连续性源自以下事实：当 \x\ 无限制地增加时，\f(x)\ 无限制地增加，这一事实从 / 的定义中显而易见。应该注意的是，这一论点对于具有多个 n 次项的 n 次多项式无效。定理 1 是以下定理的结果，该定理断言方程“本质上”有 n 个解。
The continuity of ƒ at oo follows from the fact that \f(x)\ increases without limit as \x\ increases without limit, a fact which is obvious from the definition of/. It should be noted that this argument is not valid for polynomials of degree n with more than one term of degree n. Theorem 1 is then a consequence of the following theorem which asserts that "essentially" the equation/(x) =0 has exactly n solutions.