Show if $R$ is Noetherian, then $R_S$ is Noetherian
74259
Why is the localization of a commutative Noetherian ring still Noetherian?
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
69141
Is every Noetherian module finitely generated?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
50212
$R/Ra$ is an injective module over itself
26805
Non-Noetherian 0-dimensional ring
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?
7645
Noetherian property for exact sequence
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
52966
Rings, ideals and units-proof
111348
Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
156457
Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
142699
Is $R/N(R)$ a faithfully flat $R$-module?