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Decidability of the class of all the rings $\\mathbb {Z}/m\\mathbb {Z}$ : A problem of Ax
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Decidability of the class of all the rings $\\mathbb {Z}/m\\mathbb {Z}$ : A problem of Ax
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Journal Article
Decidability of the class of all the rings $\\mathbb {Z}/m\\mathbb {Z}$ : A problem of Ax
2023
Overview
We prove that the class of all the rings
$\\mathbb {Z}/m\\mathbb {Z}$
for all
$m>1$
is decidable. This gives a positive solution to a problem of Ax asked in his celebrated 1968 paper on the elementary theory of finite fields [1, Problem 5, p. 270]. In our proof, we reduce the problem to the decidability of the ring of adeles
$\\mathbb {A}_{\\mathbb {Q}}$
of
$\\mathbb {Q}$
.
Publisher
Cambridge University Press
Subject
