A Structure Theorem for Right1 Adequate Semigroups of Type F

A right adequate semigroup of type F means a right adequate semi-group which is an F-rpp semigroup. We obtain the structure theorem for right adequate semigroups: a semigroup is a right adequate semi-group of type F if and only if it is isomorphic to some F(M,Y), where (M,Y) is an F-pair. As its applications, we establish a structure for ade-quate semigroups of type F. Our result extends the results on F-inverse semigroups. Mathematics Subject Classification: 20M1