I don't want to use the word elemental, nor axiomatic, as both terms are already defined and in popular use.
Anyway, the way I want to use the term is not to describe the part, or type of part itself, but the quality that the part possesses; 'Something with which cannot be broken down any further possesses the quality x', where x is the word I seek, in the same way an axiom has the quality of being axiomatic.