Difference between revisions of "Polynomial ring"

(New page: Given a (commutative) ring <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>.")
 
(more formal definition? do we need to prove ringness? also {{stub}})
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Given a (commutative) [[ring]] <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>."
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Given a (commutative) [[ring]] <math>R</math>, the polynomial ring <math>R[x]</math> is, informally, "the ring of all polynomials in <math>x</math> with coefficients in <math>R</math>."  
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<cmath>R[x]=\left\lbrace\sum_{i=0}^\infty a_ix^i\mid a_i\in R\right\rbrace</cmath>
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<!-- do we need to prove the ringness of R[x]?-->
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{{stub}}

Revision as of 10:40, 26 March 2009

Given a (commutative) ring $R$, the polynomial ring $R[x]$ is, informally, "the ring of all polynomials in $x$ with coefficients in $R$."

\[R[x]=\left\lbrace\sum_{i=0}^\infty a_ix^i\mid a_i\in R\right\rbrace\]


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