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On Prime bi-k-Ideals of a Ternary Semiring |
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PP: 23-28 |
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doi:10.18576/sjm/050104
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Author(s) |
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Swapnil Wani,
Kishor Pawar,
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Abstract |
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| In this paper we define and study the concepts of prime bi-k-ideals, strongly prime bi-k-ideals, semiprime bi-k-ideals, irreducible bi-k-ideals and strongly irreducible bi-k-ideals of a ternary semiring using [2], [3], [7] and [8]. We generalize the concepts of fully idempotent semiring introduced by Ahsan [1] to a fully bi-k-idempotent ternary semiring using [2] and [7]. We also prove that if the set of bi-k-ideals of a ternary semiring S is totally ordered under the set inclusion, then S is fully bi-k-idempotent if and only if each bi-k-ideal of S is prime |
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