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Given a monomial ideal I = 〈m1, m2,..., mk〉, where mi are monomials, and a polynomial f as an arithmetic circuit the monomial Ideal Membership Problem is to test if f ∈ I. We show that the problem has a randomized polynomial time algorithm for constant k. Furthermore, if k is constant and f is computed by a ΣΠΣ circuit with output gate of bounded fanin then we can test whether f ∈ I in deterministic polynomial time.