Abstract
Let be a nonempty commutative semigroup written additively. An element e of
is said to be idempotent if e + e = e. The Erdős-Burgess constant
of the semigroup
is defined as the smallest positive integer
such that any
-valued sequence T of length
contains a nonempty subsequence the sum of whose terms is an idempotent of
We make a study of
when
is a direct product of arbitrarily many of cyclic semigroups. We give the necessary and sufficient conditions such that
is finite, and we obtain sharp bounds of
in case
is finite, and determine the precise value of
in some cases which unifies some well known results on the precise value of Davenport constant in the setting of commutative semigroups.
Acknowledgements
The author is grateful to the anonymous reviewer for many helpful suggestions, which have led to substantial improvements in the presentation and arguments of the paper.