A Sheaf On The Second Spectrum Of A Module

TL;DR

This paper constructs a sheaf of modules on the second spectrum of an R-module with the dual Zariski topology, linking algebraic properties to sheaf sections and morphisms.

Contribution

It introduces a new sheaf construction on the second spectrum of modules and explores its properties and relations to module algebraic features.

Findings

Characterization of sheaf sections via ideal transform modules

Relations between algebraic properties of N and sheaf sections

Morphisms of sheaves induced by homomorphisms

Abstract

Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology of M, where N is an R-module. We give a characterization of the sections of the sheaf O(N; M) in terms of the ideal transform module. We present some interrelations between algebraic properties of N and the sections of O(N; M). We obtain some morphisms of sheaves induced by ring and module homomorphisms.