Noetherian rings have only finitely many minimal prime ideals.
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
4397
Finite rings without zero divisors are division rings.
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
92519
ideal behind Maximal ideals are Prime ideals
107002
Noetherian ring whose ideals have arbitrarily large number of generators
63568
Ring with finitely many zerodivisors
74314
Noetherian ring and the same prime divisors
149753
The structure of a Noetherian ring in which every element is an idempotent.
31585
Primary ideals of $\mathbb{Z}$
5360
Ideal contained in a finite union of prime ideals
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
69141
Is every Noetherian module finitely generated?
80616
A ring with few invertible elements
68167
Intersection of powers of an ideal in a Noetherian ring
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
116526
Finite ring has only zero divisors and units