• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.69-76
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• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.