Why prime avoidance lemma allows only at most 2 non-prime ideals?
9204
Counterexamples to the avoidance lemma for arbitrary ideals
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
19883
Prime ideals of the matrix ring
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
21862
Proof of lack of pure prime producing polynomials.
135586
Prove that the preimage of a prime ideal is also prime.
114640
Showing that an ideal is not a free $R-$module.
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
116000
Prove that prime ideals of a finite ring are maximal
91180
Show $R \setminus S$ is a union of prime ideals
133975
Localising a polynomial ring and non-maximal prime ideal
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal