Show that a ring is a division ring if it satisfies following property
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
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
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
6896
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
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
79535
Prove that $R$ is a commutative ring if $x^3=x$
154530
Rings whose elements are partitioned between units and zero-divisors.
11573
Rings and some of their properties
102086
Prove a property of divisor function
135781
Division ring if and only if it has no proper left ideals.
23521
Power Set of $X$ is a Ring with Symmetric Difference, and Intersection
87946
Proving that the unities of a ring form a group under multiplication