Primary decomposition over partially ordered groups
Abstract
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the introduction of basic notions in the relevant generality, such as closedness of partially ordered abelian groups, faces and their coprimary modules, and finiteness conditions as well local and global support functors for modules over partially ordered groups.
Cite
@article{arxiv.2008.00093,
title = {Primary decomposition over partially ordered groups},
author = {Ezra Miller},
journal= {arXiv preprint arXiv:2008.00093},
year = {2020}
}
Comments
13 pages, 5 figures. Supersedes the portion of arXiv:1908.09750 dealing with primary decomposition in partially ordered groups (which, in turn, superseded the relevant portion of arXiv:1709.08155). Material in arXiv:1908.09750 on arbitrary posets and proofs of conjectures by Kashiwara and Schapira now in separate manuscripts; they involve different background and hypotheses. v2: updated references