# On Bezout Inequalities for non-homogeneous Polynomial Ideals

## TL;DR

This paper introduces a new notion of degree for non-homogeneous polynomial ideals, establishes Bézout inequalities for ideal sums, and computes degrees probabilistically, advancing algebraic geometry tools.

## Contribution

It proposes a workable degree concept for non-homogeneous ideals and proves related Bézout inequalities, providing new theoretical insights.

## Key findings

- Defined a workable degree for non-homogeneous ideals
- Proved Bézout inequalities for ideal sums
- Developed probabilistic methods to compute degrees

## Abstract

We introduce a "workable" notion of degree for non-homogeneous polynomial ideals and formulate and prove ideal theoretic B\'ezout Inequalities for the sum of two ideals in terms of this notion of degree and the degree of generators. We compute probabilistically the degree of an equidimensional ideal.