**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**.

| | | | | created: 2014-03-02 12:30:37 | modified: 2017-08-12 14:36:01 | by: *bookofproofs*

## 1.**Definition**: Monic Polynomial

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