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Letbe a nonempty commutative semigroup written additively. An element  e  ofis said to be idempotent if  e  +  e  =  e . The Erdős-Burgess constantof the semigroupis defined as the smallest positive integersuch that any-valued sequence  T  of lengthcontains a nonempty subsequence the sum of whose terms is an idempotent ofWe make a study ofwhenis a direct product of arbitrarily many of cyclic semigroups. We give the necessary and sufficient conditions such thatis finite, and we obtain sharp bounds ofin caseis finite, and determine the precise value ofin some cases which unifies some well known results on the precise value of Davenport constant in the setting of commutative semigroups.

Erdős-Burgess constant of commutative semigroups