Morita equivalence of semigroups
B. Afara · 2012
thesis or use of any of the information contained in it must be acknowledging this thesis as the source of the quotation or information. ii Morita equivalence is a general way of classifying structures by means of their actions that is weaker than isomorphism but at the same time useful. It arose first in the study of unital rings in the 1950’s [35] but has since been extended to many other kinds of strucures, including classes of non-unital rings. It was first applied to semigroup theory in the 1970’s in the work of Banaschewski [5] and Knauer [19] who independently determined when two monoids were Morita equivalent. However they were unable to extend their definition to arbitrary semigroups since Banaschewski showed that Morita equivalence reduced to isomorphism. It was not until the 1990’s that Talwar [40, 41] was able to find a good definition of Morita equivalence for a class of semigroups that included all