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From right PP monoids to restriction semigroups: a survey. (English) Zbl 1214.20056
Summary: Left restriction semigroups are a class of semigroups which generalise inverse semigroups and which emerge very naturally from the study of partial transformations of a set. Consequently, they have arisen in a variety of different contexts, under a range of names. One of the various guises under which left restriction semigroups have appeared is that of weakly left E-ample semigroups, as studied by Fountain, Gomes, Gould and Lawson, amongst others. In the present article, we survey the historical development of the study of left restriction semigroups, from the ‘weakly left E-ample’ perspective, and sketch out the basic aspects of their theory.

MSC:
20M20 Semigroups of transformations, relations, partitions, etc.
20M18 Inverse semigroups
20M50 Connections of semigroups with homological algebra and category theory
20-03 History of group theory
01A60 History of mathematics in the 20th century
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