An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems II

TL;DR

This paper extends Furstenberg's structure theorem to Noetherian modules over syndetic rings, providing a quantitative multiple recurrence theorem applicable in this algebraic setting.

Contribution

It introduces a novel extension of Furstenberg's structure theorem tailored for Noetherian modules over syndetic rings, enabling new recurrence results.

Findings

Established a quantitative multiple recurrence theorem for Noetherian modules over syndetic rings.

Extended Furstenberg's structure theorem to a broader algebraic context.

Provided tools for analyzing recurrence phenomena in algebraic dynamical systems.

Abstract

Using a recent Furstenberg structure theorem, we obtain a quantitative multiple recurrence theorem relative to any locally compact second countable Noetherian module over a syndetic ring.