Luzius Grunenfelder and Matjaz Omladic
Ascent and descent for finite sequences of commuting endomorphisms

Homological techniques involving the Koszul complex are used to define and explore two invariants, ascent and descent, for a finite sequence of commuting endomorphism of a module. It is shown in particular that, as in the case of a single endomorphism, if ascent and descent are both finite then they are equal, and that this finiteness condition is equivalent to a certain strong Fitting type property.