A basic question about finite rings and local rings
33283
Every Artinian ring is isomorphic to a direct product of Artinian local rings
47086
Quotient rings and free modules
57732
Rings of fractions and homomorphisms
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
83115
A set of elements in a reduced unity ring
96144
Every element outside the maximal ideal of a local ring is a unit
76047
Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
1425
The Chinese Remainder Theorem for Rings.
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
90889
Prime ideals in a finite direct product of rings
94157
Normal Ring and Prime Ideal whose Square is Principal
111239
Are monomorphisms of rings injective?
97999
Explain these ring isomorphisms
45684
Is quotient of a ring by a power of a maximal ideal local?
77862
Question about fields and quotients of polynomial rings
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?