The semigroup whose bi-ideals are ideals is called I0-semigroup,the semigroup whose subsemigroups are bi-ideals is called C0-semigroup;the following results are given： the sufficient and necessary condition of regular seimgroup S being I0-semigroup is B（S） being semilattice;if the π-regular seimgroupS is C0-semigroup,Sis a nil-extension of rectangular band.
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