• COMPLETENESS FOR CONCRETE NEAR-FIELD SPACES OVER REGULAR...

Abstract

In this paper a completeness criterion for near-field spaces over a finite group of near-field sub-spaces from a clone theory. The relationship between near-field spaces and clones containing the group of near-field space operations of the underlying group of near-field space shows that the unary pair of such clones corresponds precisely to near-field spaces containing the identity function. Characterization of maximal clones is then applied to describe maximal near-field spaces containing the identity map, while maximal near-field spaces not containing the identity are described using typical methods on   near-field spaces. This finally provides us with a probability the set containing a single bijection is complete.