Abstract
We introduce the notions of quasi-ideal and bi-ideal in ternary semirings and study some properties of these two ideals. We also characterize regular ternary semiring in terms of these two subsystems of ternary semirings.
Highlights
Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal
In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups
In [2], we introduced the notion of ternary semiring
Summary
Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. An additive subsemigroup Q of a ternary semiring S is called a quasi-ideal of S if QSS ∩ (SQS + SSQSS) ∩ SSQ ⊆ Q. Right, and lateral ideal of a ternary semiring S is a quasi-ideal of S.
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