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>." | + | 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> | ||
+ | |||
+ | <!-- do we need to prove the ringness of R[x]?--> | ||
+ | |||
+ | {{stub}} |
Revision as of 10:40, 26 March 2009
Given a (commutative) ring , the polynomial ring is, informally, "the ring of all polynomials in with coefficients in ."
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