---- > [!definition] Definition. ([[homogeneous polynomial]]) > Let $R$ be a [[ring]]. A [[polynomial 4|polynomial]] $f \in R[x]$ is called **homogenous** if all nonzero terms have the same degree. ^definition > [!basicexample] > - $x^{5}+2x^{3}y^{2}+9xy^{4}$ is a homogeneous polynomial of degree $5$. > - Any element of $R$ can be viewed as a homogeneous degree-zero polynomial ^basic-example ---- #### ---- #### 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 > ```