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In this work, three particular types of semigroups are considered namely: the bisimple inverse w-semigroup, the _-bisimple type A -w semigroup and the _-bisimple type A I-semigroup. Their consideration is motivated by a construction known as the Bruck-Reilly extension of a monoid. In addition, the connection between inverse semigroups and type A semigroups as well as the properties of these types of semigroups are presented.