• 제목/요약/키워드: ternary semiring

검색결과 4건 처리시간 0.021초

Valuations on Ternary Semirings

  • Pal, Sumana;Sircar, Jayasri;Mondal, Pinki
    • Kyungpook Mathematical Journal
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    • 제62권1호
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    • pp.57-67
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    • 2022
  • In the present study, we introduce a valuation of ternary semiring on an ordered abelian group. Motivated by the construction of valuation rings, we study some properties of ideals in ternary semiring arising in connection with the valuation map. We also explore ternary valuation semirings for a noncommuative ternary division semiring. We further consider the notion of convexity in a ternary semiring and how it is reflected in the valuation map.

On Partitioning and Subtractive Ideals of Ternary Semirings

  • Chaudhari, Jaiprakash Ninu;Ingale, Kunal Julal
    • 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/$I_{(Q)}$.

A Note on Regular Ternary Semirings

  • Dutta, Tapan Kumar;Kar, Sukhendu
    • Kyungpook Mathematical Journal
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    • 제46권3호
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    • pp.357-365
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    • 2006
  • This paper is a sequel of our previous paper [1]. In this paper, we introduce the notions of regular ideal and partial ideal ($p$-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring.

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ON WEAKLY COMPLETELY QUASI PRIMARY AND COMPLETELY QUASI PRIMARY IDEALS IN TERNARY SEMIRINGS

  • Yiarayong, Pairote
    • 대한수학회논문집
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    • 제31권4호
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    • pp.657-665
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    • 2016
  • In this investigation we studied completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Some characterizations of completely quasi primary and weakly completely quasi primary ideals were obtained. Moreover, we investigated relationships between completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Finally, we obtained necessary and sufficient conditions for a weakly completely quasi primary ideal to be a completely quasi primary ideal.