Let $R$ a left artinian ring. Show that if $a \in R$ is not a right zero divisor, then $a$ is a unit in $R$.
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
66451
In a ring, how do we prove that a * 0 = 0?
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.
84751
How can it be possible to localize a ring at a set with zero divisors?
58532
If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?
138383
group of units in a topological ring
79650
Division Rings and Division Algebras
87946
Proving that the unities of a ring form a group under multiplication
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
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
140437
If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
77382
Left ideals of $M_n(K)$
15320
Morita equivalence and right and left ideals of a Ring
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$