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primitive idempotents

Proceedings of the Edinburgh Mathematical Society (1)

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Primitive inverse congruences on categorical semigroups
John Fountain, Gracinda M. S. Gomes
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 2 / June 2000

Published online by Cambridge University Press:

20 January 2009, pp. 395-413
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We give an abstract description of the kernel of a proper primitive inverse congruence on a categorical semigroup. More specifically, we show that it is a *-reflexive, *-unitary, *-dense subsemigroup, and that on a given categorical semigroup there is a one–one correspondence between such subsemigroups and the proper primitive inverse congruences. Our results allow us to give a description of the minimum proper primitive inverse semigroup congruence on a strongly E*-dense categorical semigroup.