Davenport constant of the multiplicative semigroup of the ring Z_n_1⊕...⊕Z_n_r [article]

Guoqing Wang, Weidong Gao
2016 arXiv   pre-print
Given a finite commutative semigroup S (written additively), denoted by D(S) the Davenport constant of S, namely the least positive integer ℓ such that for any ℓ elements s_1,...,s_ℓ∈S there exists a set I⊊ [1,ℓ] for which ∑_i∈ I s_i=∑_i=1^ℓ s_i. Then, for any integers r≥ 1, n_1,...,n_r>1, let R=Z_n_1⊕...⊕Z_n_r be the direct sum of these r residue class rings Z_n_1, ...,Z_n_r. Moreover, let S_R be the multiplicative semigroup of the ring R, and U(S_R) the group of units of S_R. In this paper,
more » ... prove that D( U(S_R))+P_2≤ D(S_R)≤ D( U(S_R))+δ, where P_2={i∈ [1,r]: 2 ∥ n_i} and δ={i∈ [1,r]: 2| n_i}. This corrects our previous published wrong result on this problem.
arXiv:1603.06030v1 fatcat:qukb2y2qlfaqlicgolwq6ilg6a