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## Definition: Polynomial over a Ring, Degree, Variable

A polynomial over the commutative ring $$R$$ is a term

$a_{0}+a_{1}x+a_{2}x^{2}+\cdots +a_{n}x^{n}$

with $$a_{i}\in R,\,i=0,\ldots ,n,\,n\in \mathbb {N}$$. If $$a_n\neq 0$$, then $$n$$ is called the degree of the polynomial. The symbol $$X$$ is called an indeterminate or variable.

| | | | | Contributors: bookofproofs

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