Left saturation closure for Ore localizations
Rings and Algebras
2019-03-11 v1
Abstract
In this paper, we introduce the notion of LSat, the left saturation closure of a subset of a module at a subset of the base ring, which generalizes multiple important concepts related to Ore localization. We show its significance in finding a saturated normal form for left Ore sets as well as in characterizing the units of a localized ring. Furthermore, LSat encompasses the notion of local closure of submodules and ideals from the realm of algebraic analysis, where it describes the result of extending a submodule or ideal from a ring to its localization and contracting it back again.
Cite
@article{arxiv.1903.03172,
title = {Left saturation closure for Ore localizations},
author = {Johannes Hoffmann and Viktor Levandovskyy},
journal= {arXiv preprint arXiv:1903.03172},
year = {2019}
}