A structure theorem for left restriction semigroups of type F

Abstract

A structure theorem for right adequate semigroups that are F-right abundant otherwise known as right adequate semigroups of type F was given by Cui and Guo. Here we obtain an analogous structure theorem for that of left restriction semigroups: a semigroup is a left restriction semigroup of type F if and only if it is isomorphic to some ℱ(𝑈,𝑌), where (𝑈,𝑌) is an ℱ-pair.