Zu Idealen ${\displaystyle {}{\mathfrak {a}},{\mathfrak {b}}\subseteq R}$ in einem kommutativen Ring ${\displaystyle {}R}$ nennt man das Ideal

${\displaystyle {}{\mathfrak {a}}+{\mathfrak {b}}={\left\{a+b\mid a\in {\mathfrak {a}},\,b\in {\mathfrak {b}}\right\}}\,}$

die Summe der Ideale.