The uniform word problem for commutative semigroups (UWCS) is the problem of determining from any given finite set of defining relations and any pair of words, whether the words describe the same element in the commutative semigroup defined by the relations. The effective decidability of this classical algebraic problem was first explicitly noted by Malcev [1958] and Emilichev [1958], though in retrospect this result can be seen to be contained in the earlier work of Konig [1903] and Hermann [1926] on polynomial ideals.
