Weakly U-abundant semigroups with strong Ehresmann transversals
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Dandan Yang
Abstract
The class of weakly U-abundant semigroups is an important source of non-regular semigroups, and it is well studied by semigroup theorists in recent years. An important subclass, called Ehresmann monoids, is deeply investigated by Branco, Gomes and Gould in 2014. In this paper, we are concerned with weakly U-abundant semigroups with strong Ehresmann transversals. Our aim is to give a structure theorem for such semigroups following the standard “Rees Theorem” type approach. As a direct application of the main result, we reobtain the structure theorem of abundant semigroups with quasi ideal adequate transversals by Chen in 2000.
The research was supported by Grants No. 11501430 and No. 61373174 of the National Natural Science Foundation of China, and by Grants No. JB150705 and No. XJS063 of the Fundamental Research Funds for the Central Universities, and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and by Grant No. 2016JQ1001 of the Natural Science Basic Research Plan in Shaanxi Province of China.
Acknowledgement
The author would like to thank Dr. Miklos Hartmann (University of York, UK) and the referee for reading through this paper carefully and for their valuable comments which lead to a substantial improvement of this paper.
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Articles in the same Issue
- Small-large subgroups of the reals
- Structural properties of algebras of S-probabilities
- Approximation in quantum measure spaces
- On Fibonomial sums identities with special sign functions: analytically q-calculus approach
- On the proximity of multiplicative functions to the number of distinct prime factors function
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- On the solutions of a second-order difference equation in terms of generalized Padovan sequences
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