On U-ample ω-semigroups

Abstract

The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR(T, θ), namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ∗-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.

Keywords

Bisimple inverse ω-semigroups / weakly U-abundant semigroups / Ehresmann semigroups / U-ample ω-semigroups

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg