The characterization and the product of quasi-Ehresmann transversals

Kong, Xiangjun; Wang, Pei

doi:10.2298/fil1907051k

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…By means of R and L, a spined product structure theorem is established for abundant semigroups with quasi-ideal refined generalised quasi-adequate transversals. Followed this paper, the product of quasi-ideal refined generalised quasiadequate transversals [23] and quasi-Ehresmann transversals [24] was considered.…”

Section: Lemma 16 [19]mentioning

confidence: 99%

On refined generalised quasi-adequate transversals

Kong

Wang

2021

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Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) ? VSo (b) ? 0 ? VSo (a) = VSo (b)] is investigated and thus the concept of refined generalised quasi-adequate transversals, for short, RGQA transversals is introduced. It is shown that RGQA transversals are the real common generalisations of both orthodox transversals and adequate transversals in the abundant case. Finally, by means of two abundant semigroups R and L, a spined product structure theorem for an abundant semigroup with a quasi-ideal RGQA transversal is established.

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Section: Lemma 16 [19]mentioning

confidence: 99%

On refined generalised quasi-adequate transversals

Kong

Wang

2021

Filomat

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Quasi-ideal Ehresmann transversals: The spined product structure

2021

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In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

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Abundant semigroups with weakly simplistic RGQA transversals

Wang

Kong

2023

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As the real common generalisations of both orthodox transversals and adequate transversals in abundant semigroups, the concept of refined generalised quasi-adequate transversals, briefly, RGQA transversals was introduced by Kong and Wang. In this paper, for the RGQA transversal, the necessary and sufficient condition for the sets I and ? to be bands is investigated. It is demonstrated that the sets I and ? are both bands if and only if the RGQA transversal is weakly simplistic. Moreover, the RGQA transversal So being weakly simplistic is different from So being a quasi-ideal nor the abundant semigroup S satisfying the regularity condition. Finally, by means of a quasi-adequate semigroup and a band, the structure theorem for an abundant semigroup with a weakly simplistic RGQA transversal is established.

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The characterization and the product of quasi-Ehresmann transversals

Cited by 3 publications

References 24 publications

On refined generalised quasi-adequate transversals

On refined generalised quasi-adequate transversals

Quasi-ideal Ehresmann transversals: The spined product structure

Abundant semigroups with weakly simplistic RGQA transversals

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