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The hypercore of a semigroup

Published online by Cambridge University Press:  20 January 2009

T. E. Hall  and
W. D. Munn
T. E. Hall
Affiliation:
Department of MathematicsMonash UniversityClayton, VictoriaAustralia3168
W. D. Munn
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow G12 8QW, Scotland
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In this paper the “hypercore” of a semigroup S is defined to be the subsemigroup generated by the union of all the subsemigroups of S without non-universal cancellative congruences, provided that at least one such subsemigroup exists: otherwise it is taken to be the empty set. It is shown first that if the hypercore of S is nonempty (which holds, for example, when S contains an idempotent) then it is the largest subsemigroup of S with no non-universal cancellative congruence, is full and unitary in S, and is contained in the identity class of every group congruence on S (Theorem 1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 107 - 112
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

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