1.NounAny (two-sided) ideal
I
{\displaystyle I}
such that for arbitrary ideals
P
{\displaystyle P}
and
Q
{\displaystyle Q}
,
P
Q
⊆
I
⟹
P
⊆
I
{\displaystyle PQ\subseteq I\implies P\subseteq I}
or
Q
⊆
I
{\displaystyle Q\subseteq I}
.
2.NounIn a commutative ring, a (two-sided) ideal
I
{\displaystyle I}
such that for arbitrary ring elements
a
{\displaystyle a}
and
b
{\displaystyle b}
,
a
b
∈
I
⟹
a
∈
I
{\displaystyle ab\in I\implies a\in I}
or
b
∈
I
{\displaystyle b\in I}
.