New posts in finitely-generated

Prove that the group $\mathrm{GL}(n, \mathbb{Z})$ is finitely generated [duplicate]

Tensor product of two finitely generated modules

Subgroups of $\mathrm{GL}(n,\mathbb{Z})$ which are not finitely generated

Questions about finitely generated nilpotent groups

Is $S_R$ finitely generated?

Group acting properly discontinuous but not cocompactly on a metric space

Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$? [closed]

What is $\Bbb Z^n/(a_1, \dots, a_n)$ or $\Bbb Z^n / I$ isomorphic to?

How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$

$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?

A fraction field is not finitely generated over its subdomain

Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

Ring is Noetherian if it admits a faithful finitely generated module with ACC on submodules generated by ideals

Finitely generated vs presented

$\mathbb Z[1/2]$ is not finitely generated?

Finitely generated nilpotent group where every element is of finite order is finite

Is almost any group generated by two generators?

the automorphism group of a finitely generated group

Center of finitely generated $C^\ast$-algebra

If the tensor product of two modules is free of finite rank, then the modules are finitely generated and projective