• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.221-233
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• 2009

In this article, we generalize a well-known result of Hebisch and Weinert that states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In addition, we demonstrate that if S is a finite commutative semiring such that the set of zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent or S must be a ring. An example is given to establish the existence of semirings in this latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.