Prescribed subintegral extensions of local Noetherian domains

TL;DR

This paper presents a method to construct subintegral extensions of local Noetherian domains with controlled invariants, providing a new approach that mimics Nagata idealization but results in a subring extension.

Contribution

It introduces a novel construction of subintegral extensions of local Noetherian domains with specified algebraic invariants, expanding the toolkit for ring extension analysis.

Findings

Constructed subintegral extensions with prescribed invariants

Behavior similar to Nagata idealization in an analytical sense

Provides a new method for creating subring extensions with controlled properties

Abstract

We show how subintegral extensions of certain local Noetherian domains $S$ can be constructed with specified invariants including reduction number, Hilbert function, multiplicity and local cohomology. The construction behaves analytically like Nagata idealization but rather than a ring extension of $S$, it produces a subring $R$ of $S$ such that $R \subseteq S$ is subintegral.