Commutative ring/Coset for ideal/Definition

Coset (ideal)

Let ${}R$ be a commutative ring, and let ${}I\subseteq R$ be an ideal in ${}R$. For ${}a\in R$, the subset

${}a+I={\left\{a+f\mid f\in I\right\}}\,$

is called the coset of ${}a$ to the ideal ${}I$. Every subset of this form is called a coset to ${}I$.