Finite ring with unity has $ab=1_R\implies ba=1_R$ for $a,b\in R$
48009
Left inverse implies right inverse in a finite ring
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
107821
The ring of integers of $\mathbf{Q}[i]$
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
3301
If $AB = I$ then $BA = I$
116526
Finite ring has only zero divisors and units
32108
$ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
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
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
105818
Given an associative $F$-algebra do there necessarily exist elements $a_1,a_2 \in K$ satisfying $a_1*a_2=a$?
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
106894
If a subring of a ring R has identity, does R also have the identity?
51428
Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$