Difference between revisions of "Linearised polynomial"
From Encyclopedia of Mathematics
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(also additive polynomial) |
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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( | + | 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
Linearised polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linearised_polynomial&oldid=30277