 Quotient ring

For a two-sided ideal $I$ of a ring $R$, the quotient $R/I$ has addition and multiplication induced from $R$.

In abstract algebra, a **quotient ring** (or factor ring) is a construction that allows you to create a new ring from a given ring by partitioning it into cosets of a subring. More formally, let \( R \) be a ring and \( I \) be a two-sided ideal of \( R \).