Quotient Rings

Description

Quotient Rings (Restklassenringe oder Faktorringe) are rings obtained from division by an Two-sided Ideal.

Definition (Modular Rings)

Let $R$ be a Ring and $I$ an Two-sided Ideal. We define the set $R/I=\{r+I:r\in R\}$. This has a natural induced ring structure. Two elements $a+I,b+I$ are equal if $a-b\in I$. We then also write $a\equiv b\mathrm{mod}I$

In the case $R=\mathbb{Z}$, the $\mathrm{mod}(n)$ is written as $\mathrm{mod}n$.