---- > [!definition] Definition. ([[quotient ring]]) > Let $R$ be a [[ring]] and $I$ an [[ideal]]. Form $R / I$ as a [[quotient group]] and endow it with [[binary operation|multiplication]] $(a+I)(b+I):=(ab)+I.$ > This operation is [[well-defined]] and turns $R / I$ into a [[ring]], called the **quotient ring of $R$ modulo $I$**. ^definition > [!equivalence] Derivation. > ![[characterization of quotienting a ring#^theorem]] ^equivalence ---- #### ---- #### 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 > ```