Reflexivity and connectedness

TL;DR

This paper explores how the failure of a module's semidualizing property affects the connectedness of the ring's prime spectrum, linking module reflexivity conditions to topological properties.

Contribution

It establishes a connection between reflexivity conditions of modules and the topological structure of the prime spectrum of the ring.

Findings

Failure of semidualizing property causes disconnection in the prime spectrum.

Reflexivity conditions influence the topological connectedness of the spectrum.

Provides criteria linking module properties to spectrum topology.

Abstract

Given a finitely generated module over a commutative noetherian ring that satisfies certain reflexivity conditions, we show how failure of the semidualizing property for the module manifests in a disconnection of the prime spectrum of the ring.