Proving the Nilradical of a Commutative Ring is closed under addition.
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
157420
Question about Subrings and integraly closed
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
87946
Proving that the unities of a ring form a group under multiplication
120065
Niven’s theorem proof.
112099
Polynomial ring with integral coefficients is integral
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
156878
If every commutator is idempotent, then the ring is commutative
82609
Ring such that $x^4=x$ for all $x$ is commutative
120149
Is the complement of a prime ideal closed under both addition and multiplication?
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
52966
Rings, ideals and units-proof
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
33040
Using Zorn's lemma show that $\mathbb R^+$ is the disjoint union of two sets closed under addition.
146276
Is there a ring such that the nilradical of it is not nilpotent?
16643
A slick proof that a field which is finitely generated as a ring is finite
150223
Nilradical and Jacobson's radical.