Jacobson radical of an Artinian ring is nilpotent.
103500
Nilpotent Jacobson radical
57543
Show that a matrix is nilpotent.
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
135736
Any artinian chain ring is self-injective.
63736
Every radical ideal in a Noetherian ring is a finite intersection of primes
130004
Jacobson radical equal to nilradical in $R[X]$
58532
If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?
18003
Standard example where Jacobson radical not equal nilradical
19883
Prime ideals of the matrix ring
142612
Matrix Ring of a Semisimple Ring
30714
A question on ring homomorphisms and maximal ideals.
150206
Every finitely generated algebra over a field is a Jacobson ring
77820
Roots in a polynomial ring
113512
Characteristic of nonzero commutative rings with unity
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
23392
The annihilator of a module is an ideal