If $R$ is a ring, a subset $I\subseteq R$ is an **ideal** of $R$ if $I$ is a subgroup of $R$ for $+$ and for all $a\in I$ and all $r\in R$,
$$ r\cdot a\in I \qquad\text{and}\qquad a\cdot r\in I.$$

In a polynomial ring $R[X_1,\dots,X_n]$, an ideal is **homogeneous** if it can be generated by homogeneous polynomials.

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- Review status: reviewed
- Last edited by John Cremona on 2020-10-11 11:24:27

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**History:**(expand/hide all)

- 2020-10-11 11:24:27 by John Cremona (Reviewed)
- 2018-08-06 03:58:39 by John Jones (Reviewed)

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