To obtain the characterization of regular simple ω2-semigroups,the regular simple ω2-semigroups withωd,d'-type D relations are studied.Starting from the ω-chains of groups with length(d,d')and the homomorphism from the ω-chains of groups with length(d,d')to the group,by using Bruck-Reilly expansion,the regular simpleω2-semigroups with ωd,d'-type D relations are obtained.It is proved that any regular simple ω2-semigroup withωd,d'-type D relations can be constructed by Bruck-Reilly extension,and the structure theorem of this kind of semi-groups is obtained.
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