If $R$ is a commutative ring, the nilpotents form necessarily an ideal of $R$?
54479
If $x,y$ are nilpotent and commute, $x+y $ is nilpotent.
68167
Intersection of powers of an ideal in a Noetherian ring
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
80088
What possible characteristics may a local commutative unital ring have?
79897
if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
116883
About ideals in a ring which is a $k$ vector space
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
49854
Ideals in polynomial rings generated by linear polynomials
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
128891
What is the significance of allowing nilpotents in scheme theory?
136985
Every finite commutative ring $R$ must be of the form
54916
Maximal ideal in commutative ring
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
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.
16945
Finding the Ideals of a Direct Product of Rings
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module