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Bi-ideals in k-regular and intra k-regular semirings

Anjan K. Bhuniya, Kanchan Jana (2011)

Discussiones Mathematicae - General Algebra and Applications

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.

Bi-ideal-simple semirings

Václav Flaška, Tomáš Kepka, Jan Šaroch (2005)

Commentationes Mathematicae Universitatis Carolinae

Commutative congruence-simple semirings were studied in [2] and [7] (but see also [1], [3]--[6]). The non-commutative case almost (see [8]) escaped notice so far. Whatever, every congruence-simple semiring is bi-ideal-simple and the aim of this very short note is to collect several pieces of information on these semirings.

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