Vol. 74, No. 1, 1978

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Algebraic numbers, a constructive development

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

Vol. 74 (1978), No. 1, 91–102

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
Received: 17 March 1977
Published: 1 January 1978
William H. Julian
Department of Mathematical Sciences
New Mexico State University
Las Cruces NM 88003
United States
Ray Mines, III
Fred Richman