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at both values. The clarification in the underlined part has to do with the difference between functions and polynomials. In finite characteristic you can have equality of functions without equality of polynomials - this makes the equals sign "=" ambiguous as to whether you mean as functions or
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I agree with you. However, I also want to dispute the clarity of the definition. The article first says that an additive polynomial is such that
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By the way, could you check my edits for correctness? Back then both of us were green and we fought like hell. :)
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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in some infinite field containing k, such as its algebraic closure (which looks like the
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Hmm, the structure of this article shows remarkable similarity to the
Mathworld article.
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at both values? Then, the article goes on to say that this (which looks like the merely
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Is the example under additive versus absolutely additive correct? That is, I think
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version) is equivalent to assume that this equality holds for all
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They are a subgroup in respect to addition or multiplication?
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is the order of the field, and if finite it must then be
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439:{\displaystyle \{w_{1},...,w_{m}\}\subset {\bar {k}}}
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571:Non-absolutely additive example dispute
260:be the set of its roots. Assuming that
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1254:{\displaystyle f(x)=x^{2}+x,g(x)=0}
352:{\displaystyle \{w_{1},...,w_{m}\}}
38:It is of interest to the following
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1450:Low-priority mathematics articles
682:{\displaystyle n\in \mathbb {N} }
115:Knowledge:WikiProject Mathematics
1445:Start-Class mathematics articles
1110:{\displaystyle P(a+b)=P(a)+P(b)}
944:{\displaystyle P(a+b)=P(a)+P(b)}
118:Template:WikiProject Mathematics
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869:and thus absolutely additive.
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301:) is additive if and only if
109:and see a list of open tasks.
539:23:03, 22 January 2005 (UTC)
1426:18:15, 6 January 2016 (UTC)
1048:14:45, 6 January 2016 (UTC)
862:{\displaystyle \tau ^{0}=x}
776:is a linear combination of
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1391:. However, as polynomials
1384:{\displaystyle x\in Z_{2}}
1351:{\displaystyle f(x)=g(x)}
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608:is absolutely additive.
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141:project's priority scale
1410:{\displaystyle f\neq g}
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654:{\displaystyle q=p^{n}}
601:{\displaystyle x^{q}-x}
98:WikiProject Mathematics
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1281:{\displaystyle Z_{2}}
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103:mathematics
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661:for some
545:Mathworld
291:separable
1358:for all
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1024:additive
535:contribs
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359:form a
293:, then
196:, and
139:on the
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36:scale.
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551:linas
361:group
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1044:talk
1030:and
972:and
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
