On monomial ideal rings and a theorem of Trevisan

TL;DR

This paper provides a direct proof that monomial ideal rings can be represented as the cohomology of topological spaces, with some realized through polyhedral products linked to simplicial complexes.

Contribution

It offers a direct proof of Trevisan's theorem and demonstrates realizations of certain monomial ideal rings via polyhedral products.

Findings

Monomial ideal rings are representable as topological space cohomology.

Some rings are realized by polyhedral products indexed by simplicial complexes.

Provides a new proof approach for Trevisan's result.

Abstract

A direct proof is presented of a form of Alvise Trevisan's result, that every monomial ideal ring is represented by the cohomology of topological space. Certain of these rings are shown to be realized by polyhedral products indexed by simplicial complexes.