Let $(R, +, \cdot)$ be a finite ring without zero divisors, show that $R$ has a neutral element for $\cdot$.
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
91962
In a ring $a*a=0$ then $a+a=0$
119067
Basic Ring Theory Question involving the unit element
116651
Show for any simple ring without identity, R, that R is a division ring.
37960
Zero Divisors in Direct Product of Rings
63568
Ring with finitely many zerodivisors
116000
Prove that prime ideals of a finite ring are maximal
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
48009
Left inverse implies right inverse in a finite ring
143051
Inverting noninvertible elements in a bigger 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?
124151
Finite ring extension and number of maximal ideals
154613
Showing a set of fractions is a ring
67342
Why does a minimal prime ideal consist of zerodivisors?
45484
Height unmixed ideal and a non-zero divisor
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.