Prove that a commutative ring without proper ideals is a field
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
41629
Structure of ideals in the product of two rings
100961
Ideals in valuation rings
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
135699
Questions about a commutative ring with exactly three ideals
116883
About ideals in a ring which is a $k$ vector space
69546
Example of non-commutative ring with exactly 2014 two sided-proper ideals.
151803
Prove that $R$ is commutative
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
79535
Prove that $R$ is a commutative ring if $x^3=x$
46254
Why can't the Polynomial Ring be a Field?
155745
Ideals of $\mathbb{Z}[X]$
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
57310
Prove $\mathbb{Z}$ is not a vector space over a field
24247
Ring Inside an Algebraic Field Extension