$A$ Noetherian and $f:A \rightarrow A$ suryective then $f$ inyective
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
144623
Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
90599
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
51245
$A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category
148500
Understanding this theorem and how to go about proving it surjectivity?
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
36150
Ideal in a ring of continuous functions
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain
74314
Noetherian ring and the same prime divisors
68167
Intersection of powers of an ideal in a Noetherian ring
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
62227
Is a product of two Noetherian schemes over Spec $\mathbb Z$ a Noetherian scheme?