Davenport constant for semigroups II

Let S be a finite commutative semigroup. The Davenport constant of S, denoted D(S), is defined to be the least positive integer ℓ such that every sequence T of elements in S of length at least ℓ contains a proper subsequence T′ (T′≠T) with the sum of all terms from T′ equaling the sum of all terms from T. Let q>2 be a prime power, and let Fq[x] be the ring of polynomials over the finite field Fq. Let R be a quotient ring of Fq[x] with 0≠R≠Fq[x]. We prove thatD(SR)=D(U(SR)), where SR denotes the multiplicative semigroup of the ring R, and U(SR) denotes the group of units in SR.