A commutative ring with identity is a field if and only it has no nonzero proper ideals
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
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?
27766
Comaximal ideals in a commutative ring
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
138309
Ring whose all ideals are double-sided is commutative?
89702
Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
72230
Equivalence of definitions of prime ideal in commutative ring
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
1141
Existence of totally ordered ring with zero divisors
114640
Showing that an ideal is not a free $R-$module.
34203
if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
82609
Ring such that $x^4=x$ for all $x$ is commutative
92962
Rings with $a^5=a$ are commutative