Wesselkamper, Thomas C.2013-06-192013-06-191974http://hdl.handle.net/10919/20237This paper shows that there does not exist a finite abelian semigroup <S, *> with order > 3 such that the semigroup operation is complete over S. Neither is {*} complete with constants over S. J. C. Muzio has shown that over any finite space there exists a set of two abelian semigroup operations which is complete with constants over the space. Hence Muzio's result is best possible.application/pdfenIn CopyrightTechnical reportCS74021-Rhttp://eprints.cs.vt.edu/archive/00000774/01/CS74021-R.pdf