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Kehayopulu, Niovi; Ponizovskiî, J. S.; Tsingelis, Michael

doi:10.1023/a:1020347003781

Cited by 9 publications

(2 citation statements)

References 2 publications

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“…Kehayopulu [4] introduced the notion of bi-ideals in ordered semigroups in 1992. It was shown by Kehayopulu et al [8] that an ordered semigroup is an ordered group if it has no proper bi-ideals. The minimality of bi-ideals was studied and used to characterized a particular class of ordered semigroups in [3].…”

Section: Introductionmentioning

confidence: 99%

On weakly bi-ideals in ordered semigroups and their fuzzifications

Lekkoksung¹,

Nakkhasen²

2022

J. Math. Computer Sci.

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The concept of bi-ideals in ordered semigroups is a subuniverse of ordered semigroups with certain conditions. It can be used to characterize ordered semigroups. In this paper, we extend the concept of bi-ideals to a general way, so-called weakly biideals. We consider the primitive and semiprimitive of weakly bi-ideals. Some connections between prime (semiprime) weakly bi-ideals and fuzzy prime (semiprime) weakly bi-ideals is established.

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Section: Introductionmentioning

confidence: 99%

On weakly bi-ideals in ordered semigroups and their fuzzifications

Lekkoksung¹,

Nakkhasen²

2022

J. Math. Computer Sci.

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“…Lajos characterized both regular and intra regular semigroups by bi-ideals [12] and by generalized bi-ideals [13]. Different classes of semigroups has been characterized using bi-ideals by many authors in [3,6,7,8,9,14,15,16,21].…”

Section: Introductionmentioning

confidence: 99%

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

Bhuniya¹,

Jana²

2011

Discuss. Math. - General Algebra and Applications

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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 + xa 2 x = xa 2 x. 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.

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