A saturação Lipschitz de uma álgebra

Abstract

The first description of the Lipschitz saturation of an algebra was given by (PHAM; TEISSIER, 1969) and later expanded upon by various mathematicians. Here we will recap the work done by Lipman in (LIPMAN, 1975), where he approached in a purely algebraic way (in the sense of not resorting to geometric tools) the set (which we will show to be, in fact, a ring), displaying seven initial properties and then expanding the concept to, among other things, compare such a structure with the saturation defined by Zariski, for example. Therefore, let’s review the prerequisites and demonstrate the compatibility of Lipschitz saturation with inclusions, direct limits and products, functorality, descents by plane algebras and contractions.