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A Munn type representation for DRC-restriction semigroups

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Abstract

The class of P-Ehresmann semigroups has been proposed by Jones as a common generalization of the classes of Ehresmann semigroups and regular \(^*\)-semigroups, and the class of DRC semigroups introduced by Stokes contains the class of P-Ehresmann semigroups as a proper subclass. Jones has introduced P-ample conditions for P-Ehresmann semigroups by which P-restriction semigroups are distinguished from P-Ehresmann semigroups, and obtained a fundamental representation for P-restriction semigroups by generalized Munn semigroups constructed from special projection algebras. In the present paper, we first introduce DRC-ample conditions for DRC semigroups by which DRC-restriction semigroups are discriminated from DRC semigroups. Then we propose and study generalized regular \(^\circ \)-semigroups which play the roles of regular \(^*\)-semigroups in the theory of Jones for P-restriction semigroups. Finally, we obtain a Munn type representation for DRC-restriction semigroups. Our result generalizes Jones’s representation theory for P-restriction semigroups to DRC-restriction semigroups.

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Acknowledgements

The author expresses his profound gratitude to Professor Peter R. Jones who has not only provided the author with some precious documents, but also put forward extremely valuable comments and suggestions on the writing of this manuscript. In particular, he suggested DRC-ample conditions (RGA) and (LGA) as simplifications of our original conditions, more compatible with the existing ample and P-ample conditions. The author is deeply grateful to the referee for his valuable comments and suggestions. Thanks also go to Professor Maria B. Szendrei for the timely communications. The paper is supported jointly by the Nature Science Foundations of China (12271442, 11661082) and the Nature Science Foundation of Shandong Province of China (ZR2020MA002).

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  1. Department of Mathematics, Yunnan Normal University, Kunming, 650500, Yunnan, People’s Republic of China

    Shoufeng Wang

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Wang, S. A Munn type representation for DRC-restriction semigroups. Period Math Hung 88, 148–171 (2024). https://doi.org/10.1007/s10998-023-00545-2

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