Suppose we know the presentation matrix of a module. (For simplicity: the module is over a local Noetherian ring, the ring is over a field.) For which invariants of the module some …

(A somewhat technical question, but maybe it is well known.) Consider matrices over the ring $k[[x_1,\dots,x_n]]$, whose entries vanish at the origin (i.e. belong to the maximal …

Let $M$ be a module over a local ring $(R,m)$, everything is finitely generated/presented. The fitting ideals, $I_j(M)$ carry a lot of information about the module. When do they ac …