Proving that the radical of an ideal is an ideal
38346
Commutative Ring: Nilpotent elements closed under addition?
138168
Prove: The pre-image of an ideal is an ideal.
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
54916
Maximal ideal in commutative ring
150911
Prove that the ring is Artinian and find a composition series of ideals
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
76661
Checking the maximality of a principal ideal in $R[x]$
41629
Structure of ideals in the product of two rings
116000
Prove that prime ideals of a finite ring are maximal
50445
Explaining the product of two ideals
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
18406
An ideal whose radical is maximal is primary