Geodesic
Morita-equivalence of semigroups with systems of local units
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 539-555

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Talwar in [5] formulates the criterion of Morita equivalence for semigroups with local units in terms of Morita context. In this paper the criterion of Morita equivalence is formulated and proved in terms of direct limits. 
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     author = {V. V. Neklyudova},
     title = {Morita-equivalence of semigroups with systems of local units},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a10/}
}
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V. V. Neklyudova. Morita-equivalence of semigroups with systems of local units. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 539-555. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a10/