# 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}}) |
||

Line 1: | Line 1: | ||

− | 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>." |

+ | |||

+ | <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 ."

*This article is a stub. Help us out by expanding it.*