Given a commutative ring R, an ideal I⊂R is a subset such that fg∈I whenever f∈R and g∈I and g+h∈I whenever g,h∈I. Show that if \(I \subsetneq ...Given a commutative ring R, an ideal I⊂R is a subset such that fg∈I whenever f∈R and g∈I and g+h∈I whenever g,h∈I. Show that if I⊊ is a proper ideal (ideal such that I \not= \mathcal{O}_0), then I \subset \mathfrak{m}_p, that is \mathfrak{m}_p is a maximal ideal.