Prove, that if the commutative ring has no zero divisors, then it is a field
14055
How to show that a finite commutative ring without zero divisors is a field?
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
117777
What are the zero divisors of $C[0,1]$?
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
100340
Invariant dimension property on a ring without zero divisors
133878
Ring of order $p^2$ is commutative.
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
36862
A question about proving that there is no greatest common divisor
5893
On the commutative property of multiplication (domain of integers, possibly reals)
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
74441
Zero divisors in matrix rings
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
37960
Zero Divisors in Direct Product of Rings
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
125604
Proof that $\mathbb{Z}$ has no zero divisors
46254
Why can't the Polynomial Ring be a Field?
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal