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In this paper we determine the smallest equivalence relation on a multialgebra for which the factor multialgebra is a universal algebra satisfying a given identity. We also establish an important property for the factor multialgebra (of a multialgebra) modulo this relation. 2000 Mathematics subject classification: primary 08A99; secondary 08A30, 20N20.doi:10.1017/s1446788700014671 fatcat:q4qamozs2rd3bbo655snwsi46i