Some algebraic invariants of mixed product ideals

TL;DR

This paper calculates algebraic invariants like depth and regularity for mixed product monomial ideals and characterizes when these ideals are Cohen-Macaulay, advancing understanding of their algebraic properties.

Contribution

It introduces explicit computations of invariants and a characterization of Cohen-Macaulay mixed product ideals, providing new insights into their algebraic structure.

Findings

Computed depth and regularity for mixed product ideals.

Characterized Cohen-Macaulay conditions for these ideals.

Enhanced understanding of algebraic properties of monomial ideals.

Abstract

We compute some algebraic invariants (e.g. depth, Castelnuovo - Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.