The theory of ordinal length
Commutative Algebra
2013-09-27 v1
Abstract
We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. 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.
Keywords
Cite
@article{arxiv.1309.6694,
title = {The theory of ordinal length},
author = {Hans Schoutens},
journal= {arXiv preprint arXiv:1309.6694},
year = {2013}
}
Comments
This is an incorporation of the previous ArXiv preprints arXiv:1301.6457 and arXiv:1210.3855