Let $M$ be a Noetherian $A$-module. Show that $M[x]$ is a Noetherian $A[x]$-module.
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
99198
Principal ideal and free module
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
28324
Inverse image of the sheaf associated to a module
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
46303
Example of a non-Noetherian complete local ring
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
87151
Primary ideals in Noetherian rings
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
85633
Rings of polynomials whose (partial) derivatives vanish are Noetherian?
44396
Noetherian Ring under a Homomorphism / homomorphic function / map