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POLYNOMIAL EQUIVALENCE OF FINITE RINGS
Published online by Cambridge University Press: 01 April 2014
Abstract
We prove that ${ \mathbb{Z} }_{{p}^{n} } $ and
${ \mathbb{Z} }_{p} [t] / ({t}^{n} )$ are polynomially equivalent if and only if
$n\leq 2$ or
${p}^{n} = 8$. For the proof, employing Bernoulli numbers, we explicitly provide the polynomials which compute the carry-on part for the addition and multiplication in base
$p$. As a corollary, we characterize finite rings of
${p}^{2} $ elements up to polynomial equivalence.
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- Research Article
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- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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