We all know Dirichlet's unit theorem — unit group of maximal order in quadratic number field is finitely generated of rank blah blah blah. I think it's pretty naive to expect most radical generalization to hold, namely:

Intergalactic Dirichlet unit theorem. Unit group of an associative unital ring with finitely generated additive group is finitely generated.

Is there any concrete counterexample?

The well known Dirichlet's unit theorem states that the unit group of a maximal order in a quadratic number field is finitely generated of rank blah blah blah. I think it's pretty naive to expect a most radical generalization to hold, namely:

Generalized Dirichlet unit theorem. The unit group of an associative unital ring with finitely generated additive group is finitely generated.

Is there any concrete counterexample?