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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

1.Definition: Monic Polynomial


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