Abstract
In this paper, for an arbitrary regular biordered set E, by using biorder–isomorphisms between the ω–ideals of E, we construct a fundamental regular semigroup W E called NH–semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further that W E can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroup S with the idempotent biordered set isomorphic to E, there exists a homomorphism from S to W E whose kernel is the greatest idempotent–separating congruence on S and the image is a full symmetric subsemigroup of W E . Moreover, when E is a biordered set of a semilattice E 0, W E is isomorphic to the Munn–semigroup \( T_{{E_{0} }} \); and when E is the biordered set of a band B, W E is isomorphic to the Hall–semigroup W B .
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This project is supported by the Key Research Foundations No. [1999]127 and No. [2002]48 of the Education Department of Sichuan Province and the Fundamental Application Research No. [01GY051-64] of the Department of Science and Technology of Sichuan Province
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Yu, B.J., Xu, M. A Biordered Set Representation of Regular Semigroups. Acta Math Sinica 21, 289–302 (2005). https://doi.org/10.1007/s10114-004-0490-4
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DOI: https://doi.org/10.1007/s10114-004-0490-4