R-wide semigroups with refined generalised quasi weak-adequate transversals

A class of refined generalised quasi weakly adequate transversals, namely RGQWA transversals is defined and the properties of r-wide semigroups with RGQWA transversals are studied. A spined product structure for r-wide semigroups with quasi-ideal RGQWA transversals is established by using two special subsemigroups R and L of the class of semigroups. This result not only gives a construction method for a class of r-wide semigroup, but also extends the structure theory of regular semigroups with orthodox transversals and the abundant semigroups with adequatese transversals.