Localization of an integral A-algebra is not always integral.
39201
Atiyah-Macdonald, Exercise 5.4
47096
translation invariant of integral on $\mathbb{R}$
12272
Why $a$ is not an essential singularity and how $f$ can be extended
85148
How do ideal quotients behave with respect to localization?
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
149973
Showing the following coordinate rings are not isomorphic
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
73573
image of polynomial map is not an algebraic set
4507
Localization of a ring which is not a domain
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
128489
Linearly independent elements are less than generators in a module.
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
127121
The identity cannot be a commutator in a Banach algebra?
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
11259
Prove $R\times S$ is not an integral domain
4717
The union of linear subspaces is not necessarily a subspace