Principal Ideal Domain $R$ and ideal $J\neq 0$ so that that $R/J$ have a finite number of ideals.
75899
Principal ideal domain with finitely many ideals
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
74150
Problem on the number of generators of some ideals in $k[x,y,z]$
512
Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
146801
Primary decomposition of an ideal
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
92822
Finite number of elements generating the unit ideal of a commutative ring
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
84149
Prove that an infinite ring with finite quotient rings is an integral domain
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
33245
Show that every ideal of the ring $\mathbb Z$ is principal
138882
A prime poset of ideals
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
108896
Prime ideal in a polynomial ring over an integrally closed domain
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.