Monomial algebraic and algebroid curves and their Lipschitz saturation over the ground ring

TL;DR

This paper characterizes the Lipschitz saturation of certain algebraic curves over a ring using numerical semigroups, providing explicit descriptions under mild conditions.

Contribution

It offers a new explicit description of Lipschitz saturation for algebraic and algebroid curves over rings, connecting algebraic structures with numerical semigroups.

Findings

Explicit description of Lipschitz saturation $A^*_{B,R}$

Connection between algebraic curves and numerical semigroups

Applicable under mild conditions on the ground ring

Abstract

In this article, we provide an explicit description of the Lipschitz saturation $A^*_{B,R}$ of a subalgebra $A\subseteq R[[t^{\gamma_1},\ldots, t^{\gamma_n}]]$ over a ring $R$ in terms of the numerical semigroup $\Gamma = \langle\gamma_{1},\ldots,\gamma_{n}\rangle$ with mild conditions imposed on $R$.