On the Normality of One-fibered Monomial Ideals

Abstract

This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Théorèmes 2.4 and 3.8]. Precisely, we show that if I is a monomial ideal of R = k[x1,x2,…,xd], then I is normal one-fibered if and only if for all positive integers n and all x, y in R such that xy ∈ I2n, either x or y belongs to In.