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Davenport constant of the multiplicative semigroup of the ring Z_n_1⊕...⊕Z_n_r
[article]
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,
arXiv:1603.06030v1
fatcat:qukb2y2qlfaqlicgolwq6ilg6a