The ideal $(x_1,x_2,x_3,.........)$ (with infinitely many variables) in the ring $K[x_1,x_2,x_3,....]$ is not finitely generated.
140553
An ideal which is not finitely generated
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
45484
Height unmixed ideal and a non-zero divisor
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
31585
Primary ideals of $\mathbb{Z}$
80679
Principal ideal rings that are not integral domains
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
135699
Questions about a commutative ring with exactly three ideals
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
109688
Zero-dimensional ideals and finite-dimensional algebras
75558
Counter-example for prime ideals in a non commutative ring.
65536
Finitely generated ideals in a Boolean ring are principal, why?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
124467
Can $(X_1,X_2) \cap (X_3,X_4)$ be generated with two elements from $k[X_1,X_2,X_3,X_4]$?
87382
Non-invertible elements form an ideal
95031
Find generators of the ideal of an algebraic set