Differentially trivial left Noetherian rings
We characterize left Noetherian rings which have only trivial derivations.
Differentially trivial Noetherian semiperfect rings.
Dimension homologique de modules simples
Division dans l'anneau des séries formelles à croissance contrôlée. Applications
We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove a Weierstrass-Hironaka division theorem for such subrings. Moreover, given an ideal ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.