Show that the ideal generated by a polynomial and a prime is maximal
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
63207
Zorn's lemma and maximal ideals
80232
Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
68202
Must an ideal generated by an irreducible element be a maximal ideal?
23099
Verifying that the ideal $(x^3-y^2)$ is prime
111996
Maximal and Prime Ideal in Z
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
49854
Ideals in polynomial rings generated by linear polynomials
157876
If every prime ideal is maximal, what can we say about the ring?
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
138882
A prime poset of ideals
60391
Ideal Generated by Three Elements in Polynomial Ring
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
111189
Intersection of all maximal ideals containing a given ideal
133975
Localising a polynomial ring and non-maximal prime ideal
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$