The kernel of the wreath product of semigroups

All wreath products, in the general sense, of two semigroups with completely simple kernels have completely simple kernels. Presented here are computational characterizations of the primitive idempotents of such a wreath and of the identities and inverses in subgroups of its kernel. Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant AF AFOSR 924-67.