Algebraic numbers, a constructive development

William H. Julian, Ray Mines, III and Fred Richman

Vol. 74 (1978), No. 1, 91–102

DOI: 10.2140/pjm.1978.74.91

Abstract

The theory of algebraic numbers is developed in the context of abstract fields with equality and inequality. Of classical interest is that any commutative local ring without nilpotent elements may be considered a field in this context. Procedures are given for deciding whether two complex algebraic numbers are equal or not, for factoring polynomials over algebraic number fields and for deciding whether a given algebraic number is in a given algebraic number field.

Mathematical Subject Classification 2000

Primary: 03F65

Secondary: 12L05

Milestones

Received: 17 March 1977

Published: 1 January 1978