A Characterization of Strongly Computable Finite Factorization Domains

Abstract In [4], Mileti and others study the prime and irreducible elements of strong finite factoriza-tion domains. The authors define the class of Strongly Computable Strong Finite Factorization Domains (SCSFFD) which, they show, have necessarily computable irreducible elements and a computable division algorithm. However, the question of how to best classify this class of structures is left unanswered. Our work provides a classification for SCSFFD’s by showing the existence of a computable norm where norm-form equations can be solved computably. This classification provides the intuition to extend further the notion of strong computability to Finite Factorization Domains in general.