On bi-ideals of semigroups

Iampan, Aiyared

doi:10.1134/s1995080208020042

Cited by 5 publications

(2 citation statements)

References 3 publications

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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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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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“…Iampan [4,5] has studied properties of biideals of semigroups and -semigroups. Further, Chinram [1] has defined the concepts of quasi--ideals in -semigroups.…”

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confidence: 99%

Notes on (m,n) bi-Γ-ideals in Γ-semigroups

Ansari

Khan

2011

Rend. Circ. Mat. Palermo

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The notions of quasi-ideals of rings and semigroups were introduced by Steinfeld (Acta Math. Acad. Sci. Hung. 4:289-298, 1953 and Publ. Math. (Debr.) 4:262-275, 1956) respectively. The notion of -semigroups was introduced by Sen (Proceeding of International Symposium on Algebra and Its Applications, Decker Publication, New York, 1981). Further the notion of (m, n) ideals of semigroups was introduced by Lajos (Acta Sci. Math. 22:217-222, 1961). Later on (m, n) quasi-ideals and (m, n) bi-ideals were widely studied in various algebraic structures viz. semigroups, rings and near-rings etc. In this paper we have defined (m, n) quasi--ideal and (m, n) bi--ideal in -semigroup. Including other results, we have shown that if Q is a minimal (m, n) quasi--ideal in -semigroup S then intersection of minimal m-left -ideals and minimal n-right -ideals is again a minimal (m, n) quasi--ideals.

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Minimal k-bi-ideals and strong quasi k-ideals in an ai-semiring

Bhuniya

Jana²

2018

Afr. Mat.

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On bi-ideals of semigroups

Cited by 5 publications

References 3 publications

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

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

Notes on (m,n) bi-Γ-ideals in Γ-semigroups

Minimal k-bi-ideals and strong quasi k-ideals in an ai-semiring

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