If (ideals) $J\subseteq I_1\cup\dots\cup I_n$ and $I_3,\dots,I_n$ are prime then $J\subseteq I_k$
5360
Ideal contained in a finite union of prime ideals
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
116000
Prove that prime ideals of a finite ring are maximal
155745
Ideals of $\mathbb{Z}[X]$
15904
Prime ideal and nilpotent elements
37929
Classification of prime ideals of $\mathbb{Z}[X]$
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
19883
Prime ideals of the matrix ring
587
Ideal Generated by the Union of Two Ideals
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
74537
Maximal Ideals in $K[y]$
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
17239
Find all ideals of ${\mathbb{Z}_n}$
144250
subideals of an ideal
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.