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arXiv · 1903.03172

Left saturation closure for Ore localizations

Johannes Hoffmann·Viktor Levandovskyy
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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.

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Johannes Hoffmann, Viktor Levandovskyy. 2019-03-07. Left saturation closure for Ore localizations. https://arxiv.org/abs/1903.03172

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