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Let K be a commutative hypergroup with the Haar measure μ. In the present paper we investigate whether the maximal ideals in L¹(K,μ) have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L^∞(K,μ). Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.