Abstract
We continue to develop the most general theory of one-sided fractions started in Bavula (Localizable sets and the localization of a ring at a localizable set. arXiv:2112.13447). The aim of the paper is to introduce 10 types of saturations of a set in a ring and using them to study localizations of a ring at localizable sets, their groups of units and various maximal localizable sets satisfying some natural conditions. The results are obtained for denominator sets (the classical situation), Ore sets and localizable sets.
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