Abstract
Rees matrix covers for regular semigroups were first studied by McAlister in 1984. Lawson extended McAlister's results to abundant semigroups in 1987. We consider here a semigroup whose set of regular elements forms a subsemigroup, named tight semigroups. In this paper, it is proved that an abundant semigroup is tight and locally E-solid if and only if it is an F-local isomorphic image of an abundant Rees matrix semigroup [Formula: see text] over a tight E-solid abundant semigroup T, where the entries of the sandwich matrix P of [Formula: see text] are regular elements of T. Our results enrich the result of Lawson on Rees matrix covers for a class of abundant semigroups and extend the results of McAlister on Rees matrix covers for regular semigroups.
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