Prove that every non-zero element of a finite commutative ring with unity is either a zero-divisor or a unit.
116526
Finite ring has only zero divisors and units
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
4397
Finite rings without zero divisors are division rings.
125604
Proof that $\mathbb{Z}$ has no zero divisors
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
156878
If every commutator is idempotent, then the ring is commutative
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
79535
Prove that $R$ is a commutative ring if $x^3=x$
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
84149
Prove that an infinite ring with finite quotient rings is an integral domain
26805
Non-Noetherian 0-dimensional ring
77453
A zero-dimensional ring is Noetherian?
109470
Proof of whether a specific element is in a commutative, invertible monoid.
138752
Prove the Radical of an Ideal is an Ideal