Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$.
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?
87151
Primary ideals in Noetherian rings
135699
Questions about a commutative ring with exactly three ideals
154613
Showing a set of fractions is a ring
146801
Primary decomposition of an ideal
75558
Counter-example for prime ideals in a non commutative ring.
87078
Prove the following set is an ideal of the ring $Z[x]$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
94157
Normal Ring and Prime Ideal whose Square is Principal
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
137450
Two-sided ideal generated by subset of not commutative ring
50908
Showing a Ring and an Ideal are equal