Quasi f-Ideals

TL;DR

This paper introduces quasi f-ideals, a broader class than f-ideals, providing characterizations, prime ideal descriptions, constructions, and formulas for Hilbert functions and series.

Contribution

It generalizes the concept of f-ideals to quasi f-ideals, offering new characterizations, prime ideal descriptions, and computational formulas.

Findings

Characterizations of quasi f-ideals of degree 2

Complete description of minimal prime ideals

Formulas for Hilbert function and series

Abstract

The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger than the class of all f-ideals. Apart from giving various characterizations of quasi f-ideals of degree 2, we have determined all the minimal primes ideals of these ideals. Moreover, construction of quasi f-ideals of degree 2 has been described; the formula for computing Hilbert function and Hilbert series of the polynomial ring modulo quasi f-ideal has been provided.