Abstract
Gulliksen, following Bass’s observations, extended the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. We show how to calculate this combinatorial invariant by means of the fundamental cycle of the module, thus linking the lattice of submodules to homological properties of the module. Using this, we equip each module with its canonical topology. From ordinal length, other ordinal-valued invariants can be derived, such as filtration rank.
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