Suppose that $a$ and $b$ belong to a commutative ring $R$. If $a$ is a unit of $R$ and $b^{2}=0$ . Show that $a+b$ is a unit of $R$
22563
Units and Nilpotents
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
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
135699
Questions about a commutative ring with exactly three ideals
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
18361
Does the unit generate the additive group in a unital ring with cyclic additive group?
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
92822
Finite number of elements generating the unit ideal of a commutative ring
138670
If product of finite elements in a ring is a unit then can we say each element as unit
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
89864
Units in finite polynomial rings
79650
Division Rings and Division Algebras
72507
Does $ab=1$ imply $ba=1$ in a ring?
35222
Characterizing units in polynomial rings
111824
Sum of nilpotent and element is a unit in ring?
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