$M$ is flat $\Leftrightarrow S^{-1}M$ is a flat $S^{-1}R$-module
56020
Localization and flatness
23392
The annihilator of a module is an ideal
103349
A question about a proof of Noetherian modules and exact sequences
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
105311
What is the intuition behind the name "Flat modules"?
26197
$B^n/S^{n-1}$ is homeomorphic to $S^n$
101860
Relating the normal bundle and trivial bundles of $S^n$ to the tautological and trivial line bundles of $\mathbb{R}P^n$
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
39755
In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
73662
Example of non-flat modules
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
53335
Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module