Equivalent Condition for Being a Division Ring
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
135781
Division ring if and only if it has no proper left ideals.
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
93632
Existence of a ring homomorphism implies characteristic divisibility
80616
A ring with few invertible elements
74441
Zero divisors in matrix rings
107900
A ring which has many distinct left inverses
72230
Equivalence of definitions of prime ideal in commutative ring
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
35222
Characterizing units in polynomial rings
45523
Can the product of two non invertible elements in a ring be invertible?
133738
Can a ring without a unit element have a subring with a unit element?
91294
order of quotient ring
100340
Invariant dimension property on a ring without zero divisors
82609
Ring such that $x^4=x$ for all $x$ is commutative
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?
50908
Showing a Ring and an Ideal are equal