Abstract
A subsemigroup S of a semigroup Q is a left order in Q, and Q is a semigroup of left quotients of S, if every element of Q can be written as a −1 b for some \({a, b\in S}\) with a belonging to a group \({\mathcal{H}}\)-class of Q. Characterizations are provided for semigroups which are left orders in completely 0-simple semigroups in the following classes: without similar \({\mathcal{L}}\)-classes, without contractions, \({\mathcal{R}}\)-unipotent, Brandt semigroups and their generalization. Complete discussion of two examples and an idea for a new concept conclude the paper.
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Petrich, M. Left Orders in Special Completely 0-Simple Semigroups. Results. Math. 63, 1033–1056 (2013). https://doi.org/10.1007/s00025-012-0251-0
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DOI: https://doi.org/10.1007/s00025-012-0251-0