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This tutorial will introduce listeners to many questions that can be asked about computable processes on fields, and will present the answers that are known, sometimes with proofs. This is not original work. The questions in greatest focus here include decision procedures for the existence of roots of polynomials in specific fields, for the irreducibility of polynomials over those fields, and for transcendence of specific elements over the prime subfield. Several of these questions are related to the construction of algebraic closures, making Rabin's Theorem prominent.


This is the author's accepted manuscript of the following article: Miller, Russell. "Computable Procedures for Fields." Connecting with Compautability, CiE 2021, pp 342-352. Part of Lecture Notes in Computer Science.

The final authenticated version is available online at



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