Geodesic
Bi-ideals in k-regular and intra k-regular semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 5-23

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Here we introduce the k-bi-ideals in semirings and the intra k-regular semirings. An intra k-regular semiring S is a semiring whose additive reduct is a semilattice and for each a ∈ S there exists x ∈ S such that a + xa²x = xa²x. Also it is a semiring in which every k-ideal is semiprime. Our aim in this article is to characterize both the k-regular semirings and intra k-regular semirings using of k-bi-ideals.
Keywords: k-bi-ideals, k-ideals, semiprimary subsets, k-regular semirings, intra k-regular semirings 
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Bhuniya, Anjan; Jana, Kanchan. Bi-ideals in k-regular and intra k-regular semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 5-23. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_1_a0/