A Generalization of Bi Ideals in Semirings
نویسندگان
چکیده
Bi ideals are the generalization of quasi ideals which are themselves the generalization of the so called one-sided, right and left ideals. In this paper, we define the m-bi ideals as a generalization of the bi ideals. The important properties of the m-bi ideals from the pure algebraic point of view have been described. Moreover, we present the form of the m-bi ideals generated by subsets of the semiring. On the basis of these properties, further characterizations of the semiring will be helpful.
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Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. Sioson [10] studied some properties of quasi-ideals of ternary semigroups. In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups. Quasi-ideals are generalization of right ideals, lateral ideals, and left ideals whereas bi-ideals are generalizati...
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