Counter-example: If $U \subseteq X$ is open and we have a S.E.S of Abelian sheaves, the corresponding S.E.S of rings/modules may not be exact
50391
Exact sequence of sheaves with non exact sequence of global sections
128334
Question regarding open covers in Zariski topology (distinguished opens of affine schemes are quasi-compact)
6385
Minimal counterexamples of the isomorphism problem for integral group rings
8654
Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
36921
An Open Interval and a Half-open Interval are not Homeomorphic
75558
Counter-example for prime ideals in a non commutative ring.
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
58640
$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
37479
Proper submodules of Noetherian modules are intersections of indecomposable modules
16984
Finite extension of domains : preimage of non-zero ideal is non-zero?
63701
An example of a regular function over an open set
144316
counterexample to Abel's theorem
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
43626
Open Mapping Theorem: counterexample
139176
The real line is not homeomorphic to any non-trivial product space