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Difference between revisions of "Linearised polynomial"

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(Start article, definition only)
 
(also additive polynomial)
 
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''additive polynomial''
  
 
A [[polynomial]] over a [[field]] of [[Characteristic of a field|characteristic]] $p \ne 0$ in which all monomials have exponents which are powers of $p$:
 
A [[polynomial]] over a [[field]] of [[Characteristic of a field|characteristic]] $p \ne 0$ in which all monomials have exponents which are powers of $p$:
 
$$
 
$$
L(x) = \sum_{i=0}^d a_i X^{p^i}} \ .
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L(X) = \sum_{i=0}^d a_i X^{p^i} \ .
 
$$
 
$$
 
Such polynomials are additive: $L(x+y) = L(x) + L(y)$.
 
Such polynomials are additive: $L(x+y) = L(x) + L(y)$.

Latest revision as of 19:48, 1 January 2015

2020 Mathematics Subject Classification: Primary: 12E10 [MSN][ZBL]

additive polynomial

A polynomial over a field of characteristic $p \ne 0$ in which all monomials have exponents which are powers of $p$: $$ L(X) = \sum_{i=0}^d a_i X^{p^i} \ . $$ Such polynomials are additive: $L(x+y) = L(x) + L(y)$.

How to Cite This Entry:
Linearised polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linearised_polynomial&oldid=30277