A Class Of U-Ample I-Semigroups

In this paper, we study U-ample I-semigroups and obtain its structure theorem. It is proved that a semigroup is a U-ample I-semigroup if and only if it can be expressed by WGBR(M, theta), namely, the weakly generalized Bruck-Reilly extension of a monoid. This result not only extends and amplifies the structure theorem of I-bisimple semigroups given by R.J. Warne, but also generalizes the structure theorem of *-bisimple type A I-semigroups given by Y. Shang and L. Wang in 2012.