MathDB

Prove that if

n \geq 2

and

I_ {1}, I_ {2}, \ldots, I_ {n}

are idealized in a unit-element commutative ring such that any nonempty

H \subseteq \{ 1,2, \dots, n \}

then if

\sum_ {h \in H} I_ {h}

Is ideal

I_ {2} I_ {3} I_ {4} \dots I_ {n} + I_ {1} I_ {3} I_ {4} \dots I_ {n} + \dots + I_ {1} I_ {2} \dots I_ {n-1}

also Is ideal.

Problem Statement