右自己移入的かつ右非特異的半群について

It is shown that each right self injective, right nonsingular semigroup is isomorphic to a direct product of right self-injective, right non-singular semigroups of types (I), (II), (III), (IV). The structures of those semigroups of four types are studied. In particular. it is shown that every semigroup of type (I) is a semilattice of groups. It is proved that every right self-injective, right non-singular regular semigroup is strongly left reversible. This gives another proof that every semigroup of type (I) is absolutely flat and, consequently, a semigroup amalgamation base.