Abstract
For two classes of regular O-simple semigroups, each containing the class of completely O-simple semigroups, it is shown that if the contracted algebra over a field F of a member of the class is regular (in the sense of von Neumann) then S has to be completely O-simple. In addition, necessary and sufficient conditions are given for the regularity of the contracted algebra over F of a completely O-simple semigroup.
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