Every prime ideal is maximal
116000
Prove that prime ideals of a finite ring are maximal
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
112045
A property of minimal prime ideal
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
68202
Must an ideal generated by an irreducible element be a maximal ideal?
76661
Checking the maximality of a principal ideal in $R[x]$
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
150239
In an integral domain every non-zero prime ideal is invertible implies every non-zero proper ideal is invertible.
17247
Localisation and prime ideals
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
63207
Zorn's lemma and maximal ideals
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
56800
Intersection of prime ideals
129371
Maximal ideals in the ring of real functions on $[0,1]$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$