Bi-ideals in Clifford ordered semigroup

Hansda, Kalyan

doi:10.7151/dmgaa.1195

Cited by 4 publications

(3 citation statements)

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“…A nonempty subset A of S is called a left (right) ideal [8] of S, if SA ⊆ A (AS ⊆ A) and (A] = A. A nonempty subset A is called a (two-sided)ideal of S if it is both a left and a right ideal of S. Following Kehayopulu [9], a nonempty subset B of an ordered semigroup S is called a bi-ideal of S if BSB ⊆ B and (B] = B. Hansda [4] studied algebraic properties of bi-ideals in completely regular and Clifford ordered semigroups.…”

Section: Introductionmentioning

confidence: 99%

$\pi$-inverse ordered semigroups

Jamadar

2024

Discuss. Math. - General Algebra and Applications

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Section: Introductionmentioning

confidence: 99%

$\pi$-inverse ordered semigroups

Jamadar

2024

Discuss. Math. - General Algebra and Applications

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“…Class of Clifford [4] as well as left Clifford [4] ordered semigroups are subclasses of class of regular ordered semigroups. A regular ordered semigroup S is called a Clifford (left Clifford) [4] ordered semigroup if for all a, b ∈ S there is x ∈ S such that ab ≤ bxa (ab ≤ xa). Following results have been given for the sake of convenience of general readers.…”

Section: Introductionmentioning

confidence: 99%

On the Semigroup of Bi-Ideals of an Ordered Semigroup

MALLICK¹,

Hansda²

2023

KgJMat

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The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.

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“…Mathematicians like Lee,Kang [15] and others studied these type of ideals in various ways. Author [5] characterized bi-ideals in Clifford and left Clifford ordered semigroup. Cao and XU [2] described minimal and maximal left ideals in ordered semigroup.…”

Section: Introductionmentioning

confidence: 99%

Minimal bi-ideals in regular and completely regular ordered semigroups

Hansda

2017

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Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a completely regular ordered semigroup is minimal and hence a regular ordered semigroup S is completely regular if and only if S is union its of minimal bi-ideals.

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Bi-ideals in Clifford ordered semigroup

Cited by 4 publications

References 7 publications

$\pi$-inverse ordered semigroups

$\pi$-inverse ordered semigroups

On the Semigroup of Bi-Ideals of an Ordered Semigroup

Minimal bi-ideals in regular and completely regular ordered semigroups

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