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Let I be a monomial ideal in a polynomial ring A = k[x 1 , . . . , x n ] over a field k of characteristic 0, T A/k (I) be the module of I-preserving kderivations on A and G be the n-dimensional algebraic torus on k. We compute the weight spaces of T A/k (I) considered as a representation of G. Using this, we show that T A/k (I) preserves the integral closure of I and the multiplier ideals of I.doi:10.1090/s0002-9939-09-09922-5 fatcat:6r6evzuwprgiph6z5d6di7hcaq