On Partitioning and Subtractive Ideals of Ternary Semirings
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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 → S′ is a maximal ternary semiring homomorphism, then S=ker f_((Q)) ≅ 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 ⊆ A if and only if A=I_((Q∩A)) ＝ {q ＋ I ∈ Q ∩ A} is a subtractive ideal of S=I_((Q)).
Abstract
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 → S′ is a maximal ternary semiring homomorphism, then S=ker f_((Q)) ≅ 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 ⊆ A if and only if A=I_((Q∩A)) ＝ {q ＋ I ∈ Q ∩ A} is a subtractive ideal of S=I_((Q)).
참고문헌 (12)
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