The contraction property on the relative weak normalization and Lipschitz saturation of algebras

TL;DR

This paper develops techniques to analyze the contraction property in the context of weak normalization and Lipschitz saturation of various algebra types, advancing understanding in algebraic structures.

Contribution

It introduces new methods for handling contraction properties in weak normalization and Lipschitz saturation for specific algebra classes.

Findings

Established contraction property techniques for universally injective algebras

Extended analysis to integral, radicial, and unramified algebras

Enhanced understanding of algebraic normalization and saturation processes

Abstract

Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective, integral, radicial, and unramified.