Characterization and Newton Complementary Dual of Quasi $f$-Ideals

TL;DR

This paper provides a complete characterization of quasi f-ideals of degree ≥ 2 and shows that the property of being a quasi f-ideal is preserved under Newton complementary duality for certain ideals.

Contribution

It offers a full characterization of quasi f-ideals of degree ≥ 2 and establishes the invariance of this property under Newton complementary duality for perfect generating sets.

Findings

Complete characterization of quasi f-ideals of degree ≥ 2

Quasi f-ideal property preserved under Newton duality for perfect generators

Extension of the theory of f-ideals to quasi f-ideals

Abstract

The notion of quasi $f$-ideals was first presented in $[14]$ which generalize the idea of $f$-ideals. In this paper, we give the complete characterization of quasi $f$-ideals of degree greater or equal to $2$. Additionally, we show that the property of being quasi $f$-ideals remains the same after taking the Newton complementary dual of a squarefree monomial ideal $I$ provided that the minimal generating set of $I$ is perfect.