A New Index Theorem for Monomial Ideals by Resolutions

TL;DR

This paper establishes a new index theorem for quotient modules of monomial ideals using resolutions by Bergman space-like Hilbert modules, advancing the understanding of their algebraic and analytical properties.

Contribution

It introduces a novel index theorem for monomial ideals' quotient modules via resolutions with Bergman space-like modules, bridging algebraic and functional analysis techniques.

Findings

Proved an index theorem for monomial ideal quotient modules.

Resolved monomial ideals using Bergman space-like Hilbert modules.

Connected algebraic resolutions with analytical operator theory.

Abstract

We prove an index theorem for the quotient module of a monomial ideal. We obtain this result by resolving the monomial ideal by a sequence of Bergman space like essentially normal Hilbert modules.