Davenport constant for semigroups

Abstract

Let G be a finite commutative semigroup. The Davenport constant of G is the smallest integer d such that, every sequence S of d elements in G contains a subsequence T (≠S) with the same product of S. Let $R=Z_{n_{1}}\oplus \cdots \oplus Z_{n_{r}}$ . Among other results, we determine D(R ×)−D(U(R)), where R × is the multiplicative semigroup of R and U(R) is the group of units of R.