---- > [!definition] Definition. ([[residue field]]) > If $R$ is a [[commutative ring|commutative]] [[ring]] and $\mathfrak{m}$ a [[maximal ideal]], the **residue field** is the [[quotient ring]] $k=\frac{R}{\mathfrak{m}}$, which is a [[field]]. > Often $R$ is a [[local ring]], so that $\mathfrak{m}$ is unique and we may unambiguously call $k$ the **residue field of $R$**. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```