---- > [!definition] Definition. ([[zero-divisor]]) > An element $a$ of a [[ring]] $R$ is called a **left-zero-divisor** if there exist element(s) $\textcolor{Skyblue}{b} \neq 0$ in $R$ for which $a\textcolor{Skyblue}{b}=0$. > An element $d$ of a [[ring]] $R$ is called a **right-zero-divisor** if there exist element(s) $\textcolor{LimeGreen}{c} \neq 0$ in $R$ which which $\textcolor{LimeGreen}{c}d=0$. > An element which is not a (left, right)-zero-divisor is called a **non-(left, right)-zero-divisor**. An element which is neither a left- nor a right-zero-divisor is called a **non-zero-divisor**. ^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 > ```