Let $A$ be a ring. Let $x$ nilpotent and $u$ $\in$ unit of $A$ then $(x + u)$ $\in$ unity of $A$.
22563
Units and Nilpotents
138383
group of units in a topological ring
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
1315
Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
27766
Comaximal ideals in a commutative ring
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
87078
Prove the following set is an ideal of the ring $Z[x]$
92822
Finite number of elements generating the unit ideal of a commutative ring
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
19884
The units of $\mathbb Z_4[x]$
149849
Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
133046
Showing $[L,rad(L)]$ is nilpotent.
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
113512
Characteristic of nonzero commutative rings with unity
32772
Proving units in a ring