Super-primitive elements

Ira J. Papick

Vol. 105 (1983), No. 1, 217–226

DOI: 10.2140/pjm.1983.105.217

Abstract

Given an extension, R ⊆ T, of commutative integral domains with identity, we say an element u ∈ T is super-primitive over R, if u is the root of a polynomial f ∈ R[x] with c_R(f)⁻¹ = 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 u ∈ T is called primitive over R, if u is the root of a polynomial f ∈ R[x] with c_R(f) = R.)

Mathematical Subject Classification 2000

Primary: 13B20, 13B20

Secondary: 13A15, 13G05

Milestones

Received: 18 August 1981

Published: 1 March 1983