Let $A$ a finite ring. Prove that $A$ is a field, or $A$ has zero divisors.
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
59687
Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
74441
Zero divisors in matrix rings
87078
Prove the following set is an ideal of the ring $Z[x]$
134773
A domain is a field if it has a common multiple $\!\neq\! 0$ of all elements $\!\neq\! 0$
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
52966
Rings, ideals and units-proof
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
70776
Characteristic of a field is $0$ or prime
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
36862
A question about proving that there is no greatest common divisor
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$