Geodesic
Abundant semigroups with weakly simplistic RGQA transversals
Filomat, Tome 37 (2023) no. 1, p. 155

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DOI

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 Λ to be bands is investigated. It is demonstrated that the sets I and Λ are both bands if and only if the RGQA transversal is weakly simplistic. Moreover, the RGQA transversal S o being weakly simplistic is different from S o 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.
DOI : 10.2298/FIL2301155W
Classification : 20M10
Keywords: Abundant semigroup, Quasi-adequate semigroup, Band, Weakly simplistic RGQA transversal 
Pei Wang; Xiangjun Kong. Abundant semigroups with weakly simplistic RGQA transversals. Filomat, Tome 37 (2023) no. 1, p. 155 . doi: 10.2298/FIL2301155W
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     title = {Abundant semigroups with weakly simplistic {RGQA} transversals},
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     year = {2023},
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     number = {1},
     doi = {10.2298/FIL2301155W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2301155W/}
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