Let $R$ denote a ring with identity, can an element $a\in R$ be a right divisor while it is not a left divisor?
17059
A ring element with a left inverse but no right inverse?
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
57031
Ring of fractions of $R$ is integral over $R$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
6896
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
74924
identity element of $(D_n ,\gcd)$
119067
Basic Ring Theory Question involving the unit element
37182
If an element has a unique right inverse, is it invertible?
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain
79535
Prove that $R$ is a commutative ring if $x^3=x$
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 $I=(0)$?
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
61962
Show $R$ is right-Artinian but not left-Artinian
111824
Sum of nilpotent and element is a unit in ring?
116883
About ideals in a ring which is a $k$ vector space