Are there maximal ideals of $k[x_1, x_2, \ldots]$ (infinite indeterminates) that are not $(x_1 - a_1, \ldots...)$ for $k$ algebraically closed?
89313
Maximal ideals of polynomial rings in infinitely many variables
109688
Zero-dimensional ideals and finite-dimensional algebras
17239
Find all ideals of ${\mathbb{Z}_n}$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
43774
Given distinct maximal ideals $M_1,...,M_n$, is $M_1\cdots M_n$ radical?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
22716
$A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
116883
About ideals in a ring which is a $k$ vector space
87617
Ring of $\mathbb{Z}_2$-valued functions
22610
Polynomial rings in infinitely indeterminants
104377
Maximal Ideals in Ring of Continuous Functions
18406
An ideal whose radical is maximal is primary
9204
Counterexamples to the avoidance lemma for arbitrary ideals
95031
Find generators of the ideal of an algebraic set
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.