If a ring has no zero-divisors and it contains a nonzero element $b$ such that $b^2 = b$, then show that $b$ is the unity for that ring
32741
Idempotents in a ring without unity (rng) and no zero divisors.
91129
Can there be an onto homomorphism from a ring without unity to a ring with unity?
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
144105
Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
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
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
24203
Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
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.
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
92420
Characteristic of  a Non-unital Integral Ring
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?
117777
What are the zero divisors of $C[0,1]$?
108775
Identify the ring $\mathbb {Z}[i]/(2 + i) $
4397
Finite rings without zero divisors are division rings.
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
26805
Non-Noetherian 0-dimensional ring