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A Characterization of Strongly Computable Finite Factorization Domains
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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.
Title: A Characterization of Strongly Computable Finite Factorization Domains
Description:
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.
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