  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.
