Super-primitive elements

Abstract

Given an extension, R C , of commutative integral domains with identity, we say an element u E T is super-primitive over R, if u is the root of a polynomial/ E R[x] with c R (f)~ = R, i.e., a super-primitive polynomial. The main purpose of this paper is to provide "super-primitive" analogues to some work of Gilmer-Hoffmann and Dobbs concerning primitive elements. (An element G is called primitive over R, if u is the root of a polynomial/ E R[x] with c R (f) = R.)