正則帯の特殊融合について

Let (E_1(Γ_1), E_2(Γ_2); U(Δ)) be a special amalgam of regular bands. In [2], the author showed that the amalgam (E_1(Γ_1), E_2(Γ_2); U(Δ)) is strongly embedded in a regular band whose structure semilattice is the free product of Γ_1 and Γ_2 amalgamating Δ in the class of semilattices. In this paper, we shall show that for any bundled semilattice Γ of a special amalgam (Γ_1, Γ_2 ; Δ) of semilattices, the amalgam (E_1(Γ_1), E_2(Γ_2); U(Δ)) can be embedded in a regular band whose structure semilattice is Ω.