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Strong Morita equivalence for ordered semigroups with local units. (English) Zbl 1289.06024

The author proves that for partially ordered semigroups \(S\) and \(T\) the following are equivalent.
(1) \(S\) and \(T\) are strongly Morita-equivalent,
(2) \(S\) and \(T\) have a joint enlargement,
(3) the Cauchy completions of \(S\) and \(T\) are equivalent.
Some results of M. V. Lawson [J. Pure Appl. Algebra 215, No. 4, 455–470 (2011; Zbl 1229.20060)] and L. Tart [Proc. Est. Acad. Sci. 61, No. 1, 38–47 (2012; Zbl 1263.06006)] are deduced as an application.

MSC:

06F05 Ordered semigroups and monoids
20M10 General structure theory for semigroups
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References:

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