Abstract
We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semigroups (a step that has previously proved to be awkward). We also put some earlier work of Gantos into a wider and clearer context, and pave the way for further progress.
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Communicated by Mária B. Szendrei
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Ghroda, N., Gould, V. Semigroups of inverse quotients. Period Math Hung 65, 45–73 (2012). https://doi.org/10.1007/s10998-012-4890-4
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DOI: https://doi.org/10.1007/s10998-012-4890-4