Permanence properties of splinters via ultrapower

TL;DR

This paper investigates how the splinter property behaves under various algebraic extensions and explores its characteristics in non-Noetherian rings, especially ultrapowers, to advance understanding in algebraic geometry and commutative algebra.

Contribution

It demonstrates the ascent of the splinter property along regular residue field extensions and regular maps, and analyzes splinter properties in non-Noetherian rings related to ultrapowers.

Findings

Splinter property ascends along regular residue field extensions.

Splinter property ascends along arbitrary regular maps in equal characteristic.

Studied splinter properties in non-Noetherian rings, especially ultrapowers.

Abstract

We show that the splinter property ascends along regular residue field extensions, and along arbitrary regular maps in equal characteristic. We also study the splinter property of non-Noetherian rings, especially those related to ultrapowers, to the extent necessary for our main results.